Numeracy (Questions 161-170) Show session ID Load QuizSave Quiz Welcome to the OLNA Support Numeracy Skill Builder Each question will be multiple choice There will be 4 answers to select from If you can’t figure out the answer, you should use the “Explanation of the Answer” as a guide to work out the correct response There maybe alternate ways to find these answers - this is only our suggested way. If you know another way to figure out the answer, follow that method! Click next to begin! Question 161. This bathroom scale shows Jeremy’s weight in kilograms. Which of these values is the closest to the weight shown on the scales? Explanation of answer: Explanation of Answer: Step 1: Phrased slightly differently, the question is simply asking you to round the value shown on the scale to the nearest whole number. Step 2: In this case you will need to round 68.7 to the nearest whole number so that it no longer has any decimals. Step 3: The number after the decimal point is 7, and since this is closer to 10 than it is to zero, we must round up. Step 4: To round up to the nearest whole number we must add 1 to the number in front of the decimal point, which in this case is 68. Step 5: So 68 + 1 = 69 Step 6: The correct answer is – c) 69 kg. a) 60 kg Refer to Explanation of Answer b) 65 kg Refer to Explanation of Answer c) 69 kg Correct Answer d) 70 kg Refer to Explanation of Answer None Question 162.Josh’s results in a javelin throwing contest are shown below.Ordered from the shortest throw at the top of the list to the longest throw at the bottom, what is the correct order of his throws?Explanation of answer:Step 1: This question asks you order the throws into ascending order. This means ordering them from the smallest number to the largest number.Step 2: One approach is to look for the smallest whole numbers first then order according to the decimal numbers after the whole number.Step 3: This means 35.16 m and 35.86 m are the smallest numbers. As the whole number (35) is the same we need to look at the decimals for the order, so .16 is smaller than .86.Step 4: This means that 35.16 m is smaller than 35.86 m.Step 5: The next two numbers are 36.42 m and 36.05 m. As the whole number (36) is the same we need to order the .42 and .05. The .05 is smaller so this means 36.05 m is smaller than 36.4 m.Step 6: This helps us form the ascending order of the throws. They are: 35.16 m, 35.86 m, 36.05 m and 36.42 m. This means answer d is in the correct ascending order.Step 7: The correct answer is – D A Refer to Explanation of Answer B Refer to Explanation of Answer C Refer to Explanation of Answer D Correct Answer None Question 163.A research agency was researching how many properties were sold in an inner city suburb. This is what they found:Approximately, what fraction of the total property sales is the number of Townhouses sold?Explanation of answer:Step 1: To find the answer for this question you must look at the correct type of properties asked in the question. You need to look for the values for Townhouses and total properties.Step 2: The number of Townhouses is 2,135. The total number of properties is 6,068. As the number of Townhouses is a proportion of the total number of properties, we can represent that proportion as a fraction.Step 3: To do this, form the fraction as 2,135/6,068. This is not a simplified fraction and we need to simplify it to get the answer. As we are looking for an approximate answer we can work with approximate numbers.Step 4: Lets round the two numbers to 2,000/6,000. The fraction is then easily simplified by dividing the top and bottom by 1,000. Dividing 2,000 by 1,000 = 2. Dividing 6,000 by 1,000 = 6. This means our fraction is now 2/6, which can be simplified again by dividing both the numerator and denominator by 2 to give us the simplified fraction of 1/3. This tells us that the approximate fraction of properties sold that were townhouses is 1/3.Step 5: The correct answer is – a) 1/3. a) 1/3 Correct Answer b) 2/4 Refer to Explanation of Answer c) 2/3 Refer to Explanation of Answer d) 1/5 Refer to Explanation of Answer None Question 164. Mike is going on an overnight hike. He weighs himself with his backpack. Mike then weighs himself without his backpack. How much does Mike’s backpack weigh? Explanation of answer: Step 1: This question essentially asks us what the difference is between the two weights. Step 2: To answer the question we need to subtract the smaller number from the larger number. We are fortunate that the decimals in both numbers are the same. This means that we do not have to use this number in the subtraction. Step 3: Now we need to subtract (or find the difference between the two numbers) 84 from 103. If our numbers were 84 and 104 the difference would be 20, but as our numbers are 84 and 103, that difference is one less than 20, so it is 19. Step 4: The question asks, what is the weight of his backpack. We know that the backpack weighs 19 kg. Step 5: The correct answer is – b) 19 kg. a) 18.5 kg Refer to Explanation of Answer b) 19 kg Correct Answer c) 19.5 kg Refer to Explanation of Answer d) 20 kg Refer to Explanation of Answer None Question 165. Wayne works in a part time job. He is paid $32 per hour.His is getting a 5% pay rise.How much more will Wayne be paid per hour?Explanation of answer:Step 1: To find out how much extra Wayne is being paid per hour, we must be able to manipulate percentages to find that answer. Step 2: The starting point is to find 10% of \$32. To find this, we move the decimal place one place to the left (This is 10% of \$32). This gives us \$3.20.Step 3: Now to find 5% we simply halve \$3.20 (as 5% is half of 10%). Half of \$3.20 is \$1.60.Step 4: Wayne will be paid as extra $1.60 per hour.Step 5: The correct answer is – b) $1.60 a) $1.06 Refer to Explanation of Answer b) $1.60 Correct Answer c) $3.20 Refer to Explanation of Answer d) $3.60 Refer to Explanation of Answer None Question 166. Tiffany and Caroline both work as a women’s boot makers. Tiffany makes one pair of boots every 15 minutes. Caroline’s rate is 5 pairs of boots per hour. Altogether, how many boots would they make in 4 hours? Explanation of answer: Step 1: To find the answer for this question we must figure out each individual’s rate of boot production, then add them together to get the final answer. Step 2: Firstly, we need to find out Tiffany’s production. She makes one pair of boots every 15 minutes. This means she makes 4 pairs of boots per hour (4 x 15 mins = 60 mins = 1 hour). She works for 4 hours so we multiply the 4 pairs of boots by 4 = 16 pairs of boots. Step 3: Secondly, we need to find out Caroline’s production. She makes 5 pairs of boots every hour. She works for 4 hours so we multiply the 5 pairs of boots by 4 = 20 pairs of boots. Step 4: Now we need to add both totals to find how many pairs of boots they have both made in 4 hours. 16 pairs of boots + 20 pairs of boots = 36 pairs of boots. Step 5: The correct answer is – c) 36 pairs of boots a) 6 pairs of boots Refer to Explanation of Answer b) 20 pairs of boots Refer to Explanation of Answer c) 36 pairs of boots Correct Answer d) 42 pairs of boots Refer to Explanation of Answer None Question 167. Tony bought some shade cloth for his backyard, but it needs to be cut to size. To fit the area he needs, he cuts a length exactly 1 metre and 9 centimetres. What is this length in millimetres? Explanation of answer: Step 1: This question asks us to convert from metres and centimetres to millimetres. This means we need to know how to convert from one to the other. Step 2: There are 10 millimetres in 1 centimetre. There are 1,000 millimetres in 100 centimetres, which is 1 metre in length. Step 3: 1 metre = 1,000 millimetres Step 4: 9 centimetres = 90 millimetres. Step 5: Add the 1,000 and 90 together = 1,090 millimetres. Step 6: The correct answer is – b) 1,090 millimetres. a) 1,900 mm Refer to Explanation of Answer b) 1,090 mm Correct Answer c) 1,009 mm Refer to Explanation of Answer d) 190 mm Refer to Explanation of Answer e) 109 mm Refer to Explanation of Answer None Question 168. Claudia runs every second night to work on her fitness. Her average time for her run is 1 hour and 20 minutes. Her average speed is 7 km per hour. Which expression gives the distance, in kilometres, of Claudia’s average run? Explanation of answer: Step 1: In this question we are looking at a final distance but using speed and time to find our answer as an expression. Step 2: The question states that Claudia runs for 1 hour and 20 mins at a pace of 7 km per hour. In the expressions shown, the 7 on the left hand side represents the distance covered in her first hour of running (7km). The extra 20 minutes she runs must be represented as a decimal. As 20 minutes is a one third of an hour, this is represented as a decimal as 0.33. Step 3: So if we multiply 0.33 by 7 we will find the distance Claudia runs in 20 minutes. The final expression should be written as: 7 + 0.33 x 7 Step 4: The correct answer is – d) 7 + 0.33 x 7 a) 7 + 0.20 Refer to Explanation of Answer b) 7 + 0.33 Refer to Explanation of Answer c) 7 + 0.20 x 7 Refer to Explanation of Answer d) 7 + 0.33 x 7 Correct Answer None Question 169. Sam bought a 20 kg bag of chicken feed. He has used 3.5 kg and now has 16.5 kg left. If he takes out 700 grams, how much is left in the bag? Explanation of answer: Step 1: For this question, it is important to recognise we are working with the 16.5 kg value not the 20 kg value. The 20 kg value is just there as a piece of information, but not required in the calculation. Step 2: We need to have an understanding of how many grams are in a kilogram to answer this question. There are 1,000 grams in 1 kilogram. This will help us in our calculations. Step 3: If we convert the 16.5 kilograms into grams we will have 16,500 grams. Next, we subtract 700 from 16,500. So 16,500 – 700 = 15,800 grams. We then convert back to kilograms. 15,800 ÷ 1,000 = 15.8 kilograms. ALTERNATE STEP 3: We can convert 700 grams into kilograms = 0.7 kg. We can then subtract the 0.7 kg from the 16.5 kg to get the answer. So, 16.5 kg subtract 0.7 kg = 15.8 kg Step 4: From both methods above, we can see that there is 15.8 kg chicken feed left in the bag. Step 5: The correct answer is – d) 15.8 kg a) 0.7 kg Refer to Explanation of Answer b) 7.7 kg Refer to Explanation of Answer c) 13.6 kg Refer to Explanation of Answer d) 15.8 kg Correct Answer None Question 170. Bruce had his backyard fence fall down during a storm. Temporary fencing is required while he organises to get a replacement fence. He needs 10 fencing panels to cover the fallen fence. The length of each fence panel is 2400 millimetres. There is a 5 centimetre gap between each of the panels when joined together. What will be the total length of the fencing once it has been assembled? Explanation of answer: Step 1: This question requires us to convert from millimetres and centimetres to metres. We also need to work with 2 different types of length then convert them both to metres. Step 2: The fencing panels are 2,400 millimetres in length and Bruce needs 10. To make this easier we should convert 2,400 millimetres to metres. 1,000 millimetres = 1 metre. So 2,400 millimetres = 2.4 metres. 10 panels multiplied by 2.4 metres each = 24 metres. Step 3: The gap between each panel is 5 centimetres. If we line up all 10 panels there would be 9 gaps in the line of panels. We need to multiply 5 centimetres by 9 gaps = 45 centimetres. 45 centimetres is the same as 0.45 metres. Step 4: Now let’s add the two totals together to get the total length of the fencing. 24 metres + 0.45 metres = 24.45 metres. Step 5: The correct answer is – c) 24.45 metres a) 244.5 metres Refer to Explanation of Answer b) 240.4 metres Refer to Explanation of Answer c) 24.45 metres Correct Answer d) 24.04 metres Refer to Explanation of Answer None Question 1. Fred used this tray to make muffins. If he filled the tray 3 times, how many muffins would Fred make? Explanation of Answer: Step 1: Look at the baking tray and count the amount of muffin holes. Step 2: The answer is 12 muffin holes. Step 3: The question asks if Fred fills the tray 3 times, how many muffins would he make. Step 4: This means you need to multiply 12 times 3 to get the total number of muffins. Step 5: The correct answer is – c) 36 muffins. a) 42 Refer to Explanation of Answer b) 28 Refer to Explanation of Answer c) 36 Correct Answer d) 45 Refer to Explanation of Answer None Question 2. The table below shows the attendance for the Perth Wildcats at Perth Arena from 2013 to 2016. The West Australian Newspaper reported the attendance rounded to the nearest thousand. In 2015, what attendance did the West Australian Newspaper report? Explanation of Answer: Step 1: The question asks you to look for the attendance in the 2015 season. Step 2: Look for the year – 2015 in the table and then across to the attendance figure. Step 3: The figure is 154,600. Step 4: The question says the West Australian Newspaper rounded the attendance to the nearest thousand. Step 5: You need to round 154,600 to the nearest thousand. Step 6: Look at the number in the thousands column, it is 4. Step 7: When rounding we need to look at the number on the right hand side of the number being rounded. In this case it is 6. Step 8: Because the 6 is closer to 10 we must round up the 4 in the thousands column by 1 digit to 5. This gives us 155,000. Step 9: The correct answer is – d) 155,000. a) 161 000 Refer to Explanation of Answer b) 154 000 Refer to Explanation of Answer c) 150 000 Refer to Explanation of Answer d) 155 000 Correct Answer None Question 3. Peter went shopping with a $50 note. He bought two items and received $12 change. Select the two items that Peter bought. Explanation of answer Step 1: The question says that $50 was used and $12 change was given, this means $38 was spent. You need to find out what two items added together came to $38. Step 2: Add item A and B together. $21.75 + $17.25 = $39.00. Not the correct answer. Step 3: Add item A and C together. $21.75 + $16.75 = $38.50. Not the correct answer. Step 4: Add item B and D together. $17.25 + $21.25 = $38.50. Not the correct answer. Step 5: Add item C and D together. $16.75 + $21.25 = $38.00. The correct answer. Step 6: As there are multiple combinations of items to get to the correct answer of $38, this question requires a process of elimination to determine the correct answer. This process is shown above. Step 7: The correct answer is – d) C and D. a) A and B Refer to Explanation of Answer b) A and C Refer to Explanation of Answer c) B and D Refer to Explanation of Answer d) C and D Correct Answer None Question 4. On a travel website, the travel distances between places in New Zealand are listed in a table. Approximately how many kilometres is it from Auckland to Taupo? Explanation of answer Step 1: Look at the top graph and locate the city of Auckland and the city of Taupo. Step 2: From the name of Taupo, trace left 4 places along the grey row to the Auckland column. Step 3: This number should be 279. This means it is 279 km from Auckland to Taupo. Step 4: The correct answer is – d) 279 km. a) 299 km Refer to Explanation of Answer b) 210 km Refer to Explanation of Answer c) 291 km Refer to Explanation of Answer d) 279 km Correct Answer None Question 5. Brendan bought perfume and chocolates for his sister’s birthday. The perfume cost $47 and the chocolate $16. How much in total did Brendan spend? Explanation of answer Step 1: Simply add the two values together. $47 plus $16 = $63. Step 2: The correct answer is – c) $63. a) $58 Refer to Explanation of Answer b) $61 Refer to Explanation of Answer c) $63 Correct Answer d) $67 Refer to Explanation of Answer None Question 6. Rowan used this map of Perth City when he visited Perth from Melbourne. Rowan’s hotel was listed as number 18 on the map. Which one of these attractions was closest to Rowan’s hotel? Explanation of answer Step 1: Find location 18 on the map. It is near the title Perth Railway Station. His hotel is the Medina Executive Barrack Plaza. Step 2: Determine which attraction is closest to number 18. Find all 4 attractions and their numbers using the key on the left hand side of the picture. Step 3: Number 9 (Art Gallery of Western Australia) is the closest. Note that Attractions have the number in a round dot. Step 4: The correct answer is – d) Art Gallery of Western Australia. a) Western Australian Museum Refer to Explanation of Answer b) Perth Mint Refer to Explanation of Answer c) His Majesty’s Theatre Refer to Explanation of Answer d) Art Gallery of Western Australia Correct Answer None Question 7. The length of a piece of timber is 2.4 metres. Jordan cuts it to a length of 2,150 millimetres. What length did Jordan remove? Explanation of answer Step 1: In reading the question you will need to convert the timber from metres (m) to millimetres (mm) to find the correct answer. As there is 1,000 millimetres in 1 metre, you need to multiply 2.4 m by 1,000 mm. Step 2: This gives you the original length of timber as 2,400 mm. Step 3: You must then subtract 2,150 mm from 2,400 mm. Step 4: 2,400 mm – 2,150 mm = 250 mm. Step 5: The correct answer is – c) 250 mm. a) 20.3 mm Refer to Explanation of Answer b) 242.65 mm Refer to Explanation of Answer c) 250 mm Correct Answer d) 300 mm Refer to Explanation of Answer None Question 8. Mary purchased 10 pens at $2.70 each. She paid with two $20 notes. How much change should Mary have received? Explanation of answer Step 1: Calculate 10 pens multiplied by $2.70 each. Simply move the decimal place one place to the right to give $27.00. This is how much 10 pens cost at $2.70 each. Step 2: Mary paid with two $20 notes. $20 multiplied by 2 is $40. This means she used $40 to pay for the pens. Step 3: You must subtract $27 from $40 to get the correct answer. $40 – $27 = $13. Step 4: The correct answer is – c) $13. a) $11 Refer to Explanation of Answer b) $12 Refer to Explanation of Answer c) $13 Correct Answer d) $15 Refer to Explanation of Answer None Question 9. The graph below shows the attendance at a theatre show on Friday afternoon. How many males attended the theatre show on Friday afternoon? Explanation of answer Step 1: When reading the question the key word to look for is males. Step 2: This means you must add the Boys and Men columns together to give the total amount of males attending the theatre show. Step 3: The Boys’ column is 12 people and the Men’s column is 3 people. Step 4: 12 + 3 = 15 people. Step 5: The correct answer is – b) 15. a) 11 Refer to Explanation of Answer b) 15 Correct Answer c) 18 Refer to Explanation of Answer d) 21 Refer to Explanation of Answer None Question 10. The graph below shows the attendance at a theatre show on Friday afternoon. How many more females than males attended the theatre show on Friday afternoon? Explanation of answer Step 1: When reading the question the key words to look for is how many more. Step 2: This means you must add the Girls and Women columns together to give the total amount of females attending the theatre show. This is 15 + 16 = 31 females. Step 3: Then you must add the Boys and Men columns together to give the total amount of males attending the show. This is 12 + 3 = 15 males. Step 4: To find the correct answer you must find the difference between the females and the males. Step 4: You must subtract 15 from 31 to get the difference. Step 5: 31 – 15 = 16. Step 6: The correct answer is – c) 16. a) 11 Refer to Explanation of Answer b) 14 Refer to Explanation of Answer c) 16 Correct Answer d) 19 Refer to Explanation of Answer None Question 11. Jack and his class had to prepare the gym for assembly. They had to arrange 293 chairs into rows. Each row, except the front one had 30 chairs. How many chairs did Jack and his class put in the front row? Explanation of answer Step 1: To find the correct answer for this question we must find out how many rows can be made with 30 chairs. Because the total number of chairs is an odd number we will struggle to get a whole number for the amount of rows. Step 2: This means we can round up the total number of chairs to 300, and when we divide 300 by 30 we end up with 10 rows. Step 3: However, as we have 293 chairs, we don’t have 10 rows of 30 chairs. What we do have is 9 rows with 30 chairs. If we multiply 9 by 30, this gives us 270 chairs in total. Step 4: This allows us to subtract 270 from 293 to give us our final row of chairs. Step 5: 293 -270 = 23. Step 6: The front row for the assembly is 23 chairs. Step 7: The correct answer is – c) 23. Alternate explanation: Step 1: Count in groups of 30 i.e. 1 x 30 = 30, then 2 x 30 = 60, then 3 x 30 = 90 until you get to 270 which should be 9 x 30 = 270. The last row would be 23 as 270 + 23 = 293. a) 15 Refer to Explanation of Answer b) 19 Refer to Explanation of Answer c) 23 Correct Answer d) 27 Refer to Explanation of Answer None Question 12. Stella’s pay rate on Friday is $12 per hour. On Sunday, her pay is $21 per hour. Last week she worked 10 hours on Friday and 5 hours on Sunday. How much was Stella paid for her work? Explanation of answer Step 1: To figure out Stella’s pay we must multiply her pay rate with the hours she has worked on each respective day. Step 2: For Friday we multiply $12 by 10 (hours) = $120. Step 3: For Sunday we multiply $21 by 5 (hours) = $105. Step 4: Add the two totals together to find out how much pay Stella gets. Step 5: $120 + $105 = $225. Step 6: The correct answer is – d) $225. a) $195 Refer to Explanation of Answer b) $208 Refer to Explanation of Answer c) $215 Refer to Explanation of Answer d) $225 Correct Answer None Question 13. It was 7:35pm when Olivia arrived home from work. The trip home took her 55 minutes. What time did she leave work? Explanation of answer Step 1: To figure out when Olivia left work we must subtract 55 mins from the time she arrived home. Step 2: Because 55 mins is close to 1 hour (60 mins) we can round that value to 60 mins. Step 3: By doing so we subtract 60 mins from 7:35pm and we get 6:35pm. Step 4: Remembering that we added 5 mins in rounding to 60 mins we must add 5 mins to the time of 6:35pm. Step 5: 6:35pm plus 5 mins = 6:40pm. Step 6: The correct answer is – d) 6:40pm. a) 6:55pm Refer to Explanation of Answer b) 6:51pm Refer to Explanation of Answer c) 6:43pm Refer to Explanation of Answer d) 6:40pm Correct Answer None Question 14. Steve catches public transport to travel between work and home. He catches a bus and tram in both directions. One way tickets cost $4 for the bus and $6 for the tram. Select the expression that shows Steve’s daily travel cost in dollars. Explanation of answer Step 1: To complete this answer you must use the order of operations acronym BIMDAS (brackets, indices, multiplication, division, addition and subtraction) in that order. Step 2: Before we use BIMDAS we must figure out how much it costs Steve to travel to and from work. $4 + $6 = $10 for a one way trip. The return trip would also cost $10, so Steve must pay $20 for his travel to and from work. Step 2: Looking at the answers given we would calculate brackets first, then the multiplication then addition. Let’s go through each answer. Step 3: a) 4 + 6 x 2: 6 x 2 = 12, then 12 + 4 = 16. Not the correct answer. Step 4: b) 4 x 2 + 6 x 2: 4 x 2 = 8 then 6 x 2 = 12, then 8 + 12 = 20. The correct answer. Step 5: c) (4 + 6)2: 4 + 6 = 10, then 102 = 100. Not the correct answer. Step 6: d) 2 x (4 + 6) x 2: 4 + 6 = 10, then 10 x 2 = 20, then 20 x 2 = 40. Not the correct answer. Step 7: The correct answer is – b) 4 x 2 + 6 x 2. a) 4 + 6 x 2 Refer to Explanation of Answer b) 4 x 2 + 6 x 2 Correct Answer c) (4 + 6)2 Refer to Explanation of Answer d) 2 x (4 + 6) x 2 Refer to Explanation of Answer None Question 15. A petrol station is selling unleaded petrol at $1.05 per litre. Sam arrives and fills his Four Wheel Drive car with 100 litres of unleaded petrol. Sam has a fuel discount voucher for 4 c per litre. How much does Sam pay for his tank of fuel? Explanation of answer Step 1: To answer this question we must first figure out how much it costs Sam to fill his tank. This would be 100 litres multiplied by $1.05. 100 x $1.05 = $105. Step 2: Now we must figure out how much of a discount Sam would get on his fuel purchase. Again we multiply 100 litres by $0.04 (or 4 c). 100 x $0.04 = $4. Step 3: To find the discounted price we subtract $4 from $105 to get the final answer. $105 – $4 = $101. Step 4: The correct answer is – d) $101. Alternate explanation: Step 1: Subtract the discount per litre from the undiscounted price to get $1.05 – $0.04 = $1.01 per litre, which is the discounted price per litre. Step 2: Multiply this by 100 litres to get 100 x $1.01 = $101.00 which is the correct answer. Note that multiplying by 100 simply involves shifting the decimal point two places to the right. a) $106.60 Refer to Explanation of Answer b) $105.00 Refer to Explanation of Answer c) $103.20 Refer to Explanation of Answer d) $101.00 Correct Answer None Question 16. Tim wanted to record a movie on TV. He set his DVD recorder to start recording at 9:45pm and finish at 11:20pm The movie started at 9:45pm and finished 2 hours and 5 minutes later. How many minutes of the movie were not recorded? Explanation of answer Step 1: To complete this answer you need to figure out for how long Tim set the DVD recorder to record. Step 2: The time Tim set his DVD recorder was 1 hour and 35 mins. (9:45pm to 11:15pm would have been 1 hour and 30 mins, so we need to add 5 mins more). Step 3: If the movie went for 2 hours and 5 mins and the DVD recorder was set for 1 hour and 35 mins, then all we need to do is subtract the 1 hour and 35 mins from the 2 hours and 5 mins. Step 4: 2 hrs 5 mins – 1 hr 35 mins = 30 minutes. Alternatively you can count minutes up from 1 hr 35 mins to 2 hr 5 mins. Both approaches will give you 30 minutes as the answer. Step 5: The correct answer is – c) 30 minutes. Alternate explanation: Step 1: Add 2 hours and 5 minutes to 9:45 PM to give 11:50 PM which is when the movie ended. Step 2: If the recording stopped at 11:20 PM then the amount of movie not recorded is the difference in time between 11:20 PM and 11:50 PM, which is 50 mins – 20 mins = 30 minutes. a) 55 minutes Refer to Explanation of Answer b) 43 minutes Refer to Explanation of Answer c) 30 minutes Correct Answer d) 10 minutes Refer to Explanation of Answer None Question 17. Barometers are used when measuring atmospheric air pressure. Two units commonly used for atmospheric pressure are the hectopascal (hPa) and millimetres of mercury (mmHg). What atmospheric pressure is this barometer showing in hectopascals? Explanation of answer Step 1: Look at the picture and the bottom of the barometer. There are two values, 730 mmHg which sits on the inside of the circle and the 970 hPa which sits on the outside of the circle. Step 2: The outside values are measured in hPa. Step 3: Look at the black needle and the value it is pointing at. It is after 1,010 hPa. The outer increments are increasing by one in value. The answer must be 1,012 hPa. Step 4: The correct answer is – b) 1,012 hPa. a) 1016 hPa Refer to Explanation of Answer b) 1012 hPa Correct Answer c) 762 hPa Refer to Explanation of Answer d) 758 hPa Refer to Explanation of Answer None Question 18. At a beef farm, 90 cattle were moved out of the paddock and weighed. Cattle heavier than 660 kilograms were not returned to the paddock. How many cattle were not returned to the paddock? Explanation of answer Step 1: The question states that cattle heavier than 660 kilograms were not returned to the pond. This means the cattle in the 661 – 680 and 681 – 700 range were not returned. Step 2: You need to count how many cattle were in these two categories. This is 15 + 10 = 25 cattle. Step 3: The correct answer is – c) 25. a) 61 Refer to Explanation of Answer b) 49 Refer to Explanation of Answer c) 25 Correct Answer d) 19 Refer to Explanation of Answer None Question 19. An electrician screws in a light bulb into a light fitting. To secure the bulb, the electrician turned through 2 1⁄2 revolutions. Through how many degrees did he turn the bulb? Explanation of answer Step 1: The question states that the bulb was rotated through 2½ revolutions. One revolution is 360 degrees; therefore ½ revolution is 180 degrees. Step 2: You need to add together 2 x 360 degrees (two revolutions) + 180 degrees (½ revolutions) = 900 degrees. (i.e. 360 + 360 + 180 = 900). Step 3: The correct answer is – a) 900 degrees. a) 900 degrees Correct Answer b) 720 degrees Refer to Explanation of Answer c) 540 degrees Refer to Explanation of Answer d) 360 degrees Refer to Explanation of Answer None Question 20. Laura’s computer has a 720-gigabyte (GB) hard drive The hard drive is 80% full. How much space is left on the hard drive of Laura’s computer? Explanation of answer Step 1: When figuring out the percentage for this question you should first find 10% of the total amount (720 GB). Step 2: To find 10% of 720, simply drop off the 0 from 720. Essentially we a moving the decimal point one place value to the left when we are trying to find out 10% of a value. This will give you 72. (If you multiply 72 by 10 you would get 720 which is 100% of Laura’s hard drive space). Step 3: Once you have found 10% then you need to find 20% as this is the amount of space left on the hard drive (100% – 80% = 20%). As 72 is 10% of the total we simply multiply 72 by 2 to get 20% of the total. Step 4: 72 x 2 = 144. Step 5: The correct answer is – c) 144 GB. a) 70 GB Refer to Explanation of Answer b) 72 GB Refer to Explanation of Answer c) 144 GB Correct Answer d) 288 GB Refer to Explanation of Answer None Question 21. Cathy uses her iPad timer when she gives her class 1 minute quick quizzes. According to Cathy’s iPad timer, there is 24 seconds remaining and 36 seconds have past. What fraction of the minute is left? Explanation of answer Step 1: To find out the fraction of a minute you need to be working with 60 seconds as the whole number. 1⁄2 of 60 seconds is 30 seconds. 1⁄3 of 60 seconds is 20 seconds. 1⁄5 of 60 seconds is 12 seconds. 12 seconds fits nicely into 24 and 36 seconds on the timer. Step 2: So 1 x 12 sec = 12 sec, 2 x 12 sec = 24 sec, 3 x 12 sec = 36 sec, 4 x 12 sec = 48 sec and 5 x 12 sec = 60 sec. Step 3: There is 24 seconds left on the timer, which means 2⁄5 of the minute is left. Step 4: The correct answer is – b) 2⁄5 of the minute. a) 1/4 of the minute Refer to Explanation of Answer b) 2/5 of the minute Correct Answer c) 3/5 of the minute Refer to Explanation of Answer d) 1/12 of the minute Refer to Explanation of Answer None Question 22. Sam paid $72 for 1.2 kilograms of fish. How much did the fish cost per 100 grams. Explanation of answer Step 1: To answer this type of question you need to work with the dollar answers as the cents answers are too small and would never equal $72. Step 2: If the fish cost $72 and weighed 1.2 kg, then we can say that there are 12 lots of 100 grams in the fish. If this is the case then $72 divided by 12 would give us an answer of $6. To check that the answer is not $6.60 we need to multiply by 12, which would give us a total of $79.20 which isn’t the correct answer. Step 3: $72 ÷ 12 = $6. Step 4: The correct answer is – b) $6.00 per 100g. a) $6.60 per 100g Refer to Explanation of Answer b) $6.00 per 100g Correct Answer c) $0.66 per 100g Refer to Explanation of Answer d) $0.60 per 100g Refer to Explanation of Answer None Question 23. Hannah has a part time job with a regular pay rate of $20 per hour. On Sundays her pay rate is 1.5 times the regular pay rate. Last week, she worked: 7 hours on Tuesday 5 hours on Wednesday and 3 hours on Sunday What should be Hannah’s pay for her work last Sunday? Explanation of answer Step 1: To answer this question you need to figure out Hannah’s pay rate for a Sunday. Her pay rate for Sunday is 1.5 times $20. Step 2: 1 x $20 = 20, 0.5 x $20 = $10. $20 + $10 = $30. Step 3: Once you have figured out the pay rate you need to multiply it by the number of hours she has worked on a Sunday, which is 3 hours. Step 4: $30 x 3 hours = $90. Step 5: The correct answer is – a) $90. a) $90 Correct Answer b) $95 Refer to Explanation of Answer c) $100 Refer to Explanation of Answer d) $110 Refer to Explanation of Answer None Question 24. Hannah has a part time job with a regular pay rate of $20 per hour. On Sundays her pay rate is 1.5 times the regular pay rate. Last week, she worked: 7 hours on Tuesday 5 hours on Wednesday and 3 hours on Sunday For her work last week, Hannah’s total pay should be? Explanation of answer Step 1: To answer this question you need to figure out Hannah’s pay rate for all three days. As we have figured out Hannah’s pay for a Sunday (which is $90) we just need to figure out how much she is pay for Tuesday and Wednesday. Step 2: Tuesday: 7 hrs x $20 = $140. Step 3: Wednesday: 5 hrs x $20 = $100. Step 4: Sunday: 3 hrs x $30 = $90. Step 5: Add all three values together to get the answer. $140 + $100 + $90 = $330. Step 6: The correct answer is – b) $330. a) $300 Refer to Explanation of Answer b) $330 Correct Answer c) $350 Refer to Explanation of Answer d) $390 Refer to Explanation of Answer None Question 25. Jacob buys tin fencing to enclose his vegetable patch. The size of the vegetable patch is 3 m x 2 m. He decides to buy 10% more fencing than the required length. How many metres of tin fencing did Jacob decide to buy? Explanation of answer Explanation of Answer: Step 1: To answer this question you need to figure out the length of the tin fencing and to understand what a rectangle is. A rectangle has two long sides, which in this case are 3 m long, and two short sides which are 2 m long. Step 2: The total length is (3 m x 2) + (2 m x 2) = (6 m + 4 m) = 10 m. Step 3: To find out the extra 10% that he bought, we need to find out 10% of 10 m. Step 4: If we were to use a calculator we would divide 10 by 10 and this would give us 1 m as the answer. Essentially we are moving the decimal point one place value to the left when we trying to find out 10% of a value. For example 10% of 64 m would be 6.4 m. Step 5: Jacob’s tin fencing needs 10 m of tin. The extra 10% he requires would be 1 m. We need to add these values to get the final answer. Step 6: 10 m + 1 m = 11 m. Step 7: The correct answer is – c) 11 m. a) 10 m Refer to Explanation of Answer b) 11 m Refer to Explanation of Answer c) 12 m Correct Answer d) 15 m Refer to Explanation of Answer None Question 26. Caitlin buys a 2 litre container full of fish oil tablets. The total amount of fish oil is 2 litres. Each tablet has 50 millilitres of fish oil. She takes one per day. How many days will the container last? Explanation of answer Step 1: The question says Caitlin buys a 2 litre container of fish oil tablets and that each tablet is 50 millilitres. You need to convert litres into millilitres when answering this question. 1 litre = 1,000 millilitres and 2 litres = 2,000 millilitres. Step 2: The question also states that she takes 1 tablet a day. This means she takes 50 millilitres of fish oil per day. Step 3: To find out how many days the tablets would last we use the smaller amount of 1,000 millilitres to start our calculations. We would start by dividing 1,000 mL by 50 mL. This could be difficult without a calculator so if we make it 2 tablets at 100 mL a day we would divide 1,000 mL by 100 mL which would give 10 days. Because 50 mL is half of 100 mL it would mean that the tablets would last twice as long (20 days). This means that if her container was a 1 litre container it would last 20 days. Step 4: As it is a 2 litre container we would double the amount of days to get the final amount. 20 days multiplied by 2 = 40 days. Step 5: The correct answer is – c) 40 days. a) 20 days Refer to Explanation of Answer b) 35 days Refer to Explanation of Answer c) 40 days Correct Answer d) 60 days Refer to Explanation of Answer None Question 27. The frame around a rectangular painting is 10cm wide. The outside dimensions of the frame are as shown in the image below. What are the inside dimensions of the frame? Explanation of answer Step 1: The frame of the picture is 10 cm per side. This means that both top and bottom (and left and right sides) sides would equal 20 centimetres in width. Step 2: This means that we need to subtract 20 cms from each side to find out the inside dimensions of the picture. Step 3: 2.3 m converts into 230 cm and 1.9 m converts into 190 cm. (1 m = 100 cm) Step 4: 230 cm minus 20 cm = 210 cm. Step 5: 190 cm minus 20 cm = 170 cm. Step 6: This means the inside dimensions of the picture is 210 cm by 170 cm. Step 7: The correct answer is – a) 210 cm by 170 cm. a) 210 cm by 170 cm Correct Answer b) 210 cm by 180 cm Refer to Explanation of Answer c) 220 cm by 180 cm Refer to Explanation of Answer d) 230 cm by 190 cm Refer to Explanation of Answer None Question 28. Darcy is the captain of the Devils cricket team. Before the game a coin is tossed to determine who is batting and who is fielding. Darcy has lost the toss in each of the last 4 games. What is the chance that he wins the next toss? Explanation of answer Step 1: This is a trick question, by putting in the fact that Darcy has lost the last 4 tosses doesn’t mean anything. He could have called ‘heads’ or ‘tails’ in any combination over the last 4 games. Step 2: What matters is that in this game he has one coin that he could call ‘heads’ or ‘tails’ on. This is a fifty – fifty chance of calling the correct side of the coin. Step 3: The correct answer is a) – Fifty – fifty. a) Fifty – fifty Correct Answer b) Unlikey Refer to Explanation of Answer c) Likely Refer to Explanation of Answer d) Impossible Refer to Explanation of Answer None Question 29. Jenna wants to fertilise her backyard lawn. The lawn is a rectangle shape, 5 m by 8 m. The instructions on the fertiliser bag are: How many handfuls of fertiliser will Jenna need? Explanation of answer Step 1: First we need to figure out how large Jenna’s lawn is. We need to multiply 8 m by 5 m to give 40 square metres. Step 2: Next we must figure out how many handfuls it will take to cover that lawn. Step 3: We use the rule of the instructions on the bag – 1 handful equals 2.5 sq. metres coverage. Step 4: We should use this approach 1 x 2.5 = 2.5 m, 2 x 2.5 = 5 m, 3 x 2.5 = 7.5 m, and 4 x 2.5 = 10 m. This means Jenna would use 4 handfuls for 10 sq. metres coverage. We simply multiply 4 handfuls by 4 lots of 10 sq. metres coverage (4 x 10 m to get 40 square metres) to give us 16 handfuls of fertiliser required. Step 5: The correct answer is – b) 16 handfuls. a) 12 handfuls Refer to Explanation of Answer b) 16 handfuls Correct Answer c) 22 handfuls Refer to Explanation of Answer d) 30 handfuls Refer to Explanation of Answer None Question 30. This table shows the approximate driving times between places in Western Australia. Daniel wants to drive from Perth to Mandurah, then Mandurah to Collie and then Collie to Busselton. What is Daniel’s total driving time? Explanation of answer Step 1: Note that you cannot just assume the correct answer to be the driving time tabulated for the trip from Perth to Busselton (3 hours) since the route specified in the question may not be the most direct route to drive between the two cities. Step 2: Look at the left hand column and find Perth, look along the row until you find the Mandurah column and the figure in that row. It is 1 hour. Step 3: Look at the left hand column and find Mandurah, look along the row until you find the Collie column and the figure in that row. It is 1.5 hours. Step 4: Look at the left hand column and find Collie, look along the row until you find the Busselton column and the figure in that row. It is 1 hour. Step 5: Add those values together. 1 hour + 1.5hours + 1 hour = 3.5 hours. Step 6: The correct answer is – d) 3.5 hours. a) 2 hrs Refer to Explanation of Answer b) 2.5 hrs Refer to Explanation of Answer c) 3 hrs Refer to Explanation of Answer d) 3.5 hrs Correct Answer None Question 31. Peter works as a window cleaner. To calculate the price of a cleaning job he must charge for several areas of his work: $20 per hour for his labour The cost of materials used GST, which is 10% of the total. A job takes Peter 4 hours and he uses $10 worth of materials. How much should he charge for the job? Explanation of answer Step 1: Calculate the total pay for 4 hours work. 4 hrs x $20 = $80. Step 2: The cost of the materials is $10 for the job. This means that he has $80 for labour and $10 for materials. We need to add this together: $80 + $10 = $90. Step 3: We need to add 10% GST to the total now we have the other costs calculated. To find 10% we move the decimal point one place value to the left and we get $9.00, which is 10% of $90. Step 4: We now need to add the $90 and $9 together to get the final cost of the job. $90 + $9 = $99. Step 5: The correct answer is – d) $99. a) $78 Refer to Explanation of Answer b) $86 Refer to Explanation of Answer c) $92 Refer to Explanation of Answer d) $99 Correct Answer None Question 32. Jack made a sand pit for his children. The dimensions of the sand pit are as shown in the image below. To fill 2⁄3 of the sand pit, how many cubic metres (m3) does Jack need to order? Explanation of answer Step 1: To calculate how much sand is needed, we must first find out how much sand the pit can hold. This is done by simply multiplying all three values. Step 2: 3 m x 5 m x 2 m = 15 x 2 = 30 m3. The pit can hold 30 m3 of sand. Step 3: To find out what 2⁄3 of the pit is, we first work out what 1⁄3 of the pit is by dividing 30 m3 by 3 which is 30 m3 ÷ 3 = 10 m3. So if 1⁄3 of the pit is 10 m3, then 2⁄3 of the pit must be 10 m3 x 2 = 20 m3. Step 4: The correct answer is – c) 20 m3. a) 10 m3 Refer to Explanation of Answer b) 17 m3 Refer to Explanation of Answer c) 20 m3 Correct Answer d) 24 m3 Refer to Explanation of Answer None Question 33. Joseph needs to buy ice-cream for a children’s party. He can make 12 ice-creams from 2 litres. He needs to make 60 ice-creams for the party. How many litres does he need to buy? Explanation of answer Step 1: To calculate how much ice-cream is needed we need to understand that 2 litres makes 12 ice-creams. We are working in multiple of 12’s to get to 60 ice-creams. Step 2: We can simply divide 60 by 12 = 5. Joseph needs 5 tubs of ice-cream for the party. However, each tub is 2 litres and we need to figure out how many litres are required. Step 3: This can be done by multiplying 5 tubs by 2 litres = 10 litres. Step 4: The correct answer is – d) 10 litres. a) 3 Litres Refer to Explanation of Answer b) 5 Litres Refer to Explanation of Answer c) 8 Litres Refer to Explanation of Answer d) 10 Litres Correct Answer None Question 34. Steve had a shed that was becoming cluttered. He decided that he would hang some of his tools from a tool rack. In one section of the rack he could only fit 5 tools. Each tool needed a hook to hang on. The first and last hooks had to be 4 centimetres from the edge of the rack, and The distance between all 5 hooks had to be the same distance. The tool rack was 58cm long. How far apart was each hook from each other? Explanation of answer Step 1: Firstly the rack is 58 cm long. The first and last hooks must be 4 cms from the edge. This means that we can subtract the 4 cm from each end, 58 cm – 4 cm – 4 cm = 50 cm. Step 2: With 50 cm remaining on the board, there needs to be 5 hooks with the same distance between each hook. Step 3: We need to place the first and last hooks at the points 4cm from the end of the board. This leaves 3 hooks to fill into the remaining space of the board. To find out the distance between each hook we need to divide 50 cm by the 4 spaces between each hook. Step 4: 50 divided by 4 = 12.5 cm. To get this answer we can divide 40 cm by 4 = 10 cm and then divide 10 cm by 4 = 2.5 cm. Add the 10 cm and 2.5 cm together = 12.5 cm. The distance between each hook is 12.5 cm. Step 5: The correct answer is – c) 12.5 cm. a) 7.5 cm Refer to Explanation of Answer b) 10.5 cm Refer to Explanation of Answer c) 12.5 cm Correct Answer d) 15.0 cm Refer to Explanation of Answer None Question 35. The graph below shows Sophie’s monthly budget. Sophie budgets $150 for food. How much does she budget for entertainment? Explanation of answer Step 1: When working with a pie chart we have to work with degrees. From there we can work back to find out a dollar amount. Step 2: The place to start is with the food section. Sophie pays $150 for food for 100° of the chart. To find 1° of the total cost we divide $150 by 100° = $1.50. This means that for every degree of the pie chart equals $1.50 of her monthly budget. Step 3: To find out how much Sophie spends on entertainment we need to find out how many degrees that section of the pie chart is. A circle is 360°, so we add the known values of 100°, 150° and 30° together to get 280°. We then need to subtract 280° from 360°. Step 4: 360° – 280° = 80°. Step 5: We now know that the entertainment section is 80° of the pie chart. We also know that 1° equals $1.50 of the budget. So to find how much Sophie allocates for entertainment we multiply 80° by $1.50 = $120. Step 6: The correct answer is – c) $120. a) $80 Refer to Explanation of Answer b) $100 Refer to Explanation of Answer c) $120 Correct Answer d) $160 Refer to Explanation of Answer None Question 36. Alex is painting his living room. He needs to buy: Drop sheets and paint materials worth $48 4 tins of paint which are $85 each, and Paint rollers, $8 per roller He wants to spend no more than $440 for these materials. What is greatest number of rollers he can buy? Explanation of answer Step 1: We know that Alex can’t spend more than $440, but has already spent money on materials and paint. We need to figure out how much for those items. Step 2: 4 paint tins: 4 x $85 = $340 (4 x 80 = $320, 4 x $5 = $20, $320 + $20 = $340). Step 3: Materials = $48. We need to add $340 + $48 = $388. Step 4: To find out how much money we have for rollers we need to subtract $440 – $388. Step 5: $440 – $388 = $52 ($440 – $50 = $390, $390 – $2 = $388). Alex has $52 to buy rollers. Step 6: We use multiples of $8 to find out how many rollers Alex can buy. i.e. 1 x $8 = $8, 2 x $8 = $16, 3 x $8 = $24, 4 x $8 =$32, 5 x $8 = $40, 6 x $8 = $48, 7 x 8 = $56. Step 7: 7 rollers will cost him $56, which won’t fit under his budget. He can only buy 6 rollers, as this costs $48. To check our total costs: $388 + $48 = $436. This means that he is under the $440 budget. Step 8: The correct answer is – c) 6 rollers. a) 3 rollers Refer to Explanation of Answer b) 5 rollers Refer to Explanation of Answer c) 6 rollers Correct Answer d) 8 rollers Refer to Explanation of Answer None Question 37. Ray and Jason work at a local convenience store. Jason’s wage is $1200. One-quarter of Jason’s wage is the same as half of Ray’s wage. What is Ray’s wage? Explanation of answer Step 1: To answer this question we must first find out what is one quarter of $1,200. Half would be $600, so a half of that is $300 (which is a quarter of $1,200). Step 2: The next step is to find out what Ray’s wage is. The question states one quarter of Jason’s wage is the same as half of Ray’s wage. This means we can double the $300 (which is a quarter of Jason’s wage) to find out what Ray’s wage is. 2 x $300 = $600. So Ray’s wage is $600. Step 3: The correct answer is – c) $600. a) $300 Refer to Explanation of Answer b) $400 Refer to Explanation of Answer c) $600 Correct Answer d) $900 Refer to Explanation of Answer None Question 38. A computer screen is a rectangle, 40 cm by 30 cm. What is the area of the screen in square metres (m2)? Explanation of answer Step 1: When working with figures that need conversion it is best to know some base measurements. For example: 1 m by 1 m = 1 m2 and 1 m x 0.5 m = 0.5 m2. Step 2: In this case we are working with centimetres so we know that the answer won’t be 1 m2 or above. The numbers are smaller than 1 m so the answer will be less than 1 m2. 40 cm is the same as 0.4 m and 30 cm is the same as 0.3 m. Step 3: To get the answer we must multiply 0.4 m by 0.3 m = 0.12 m2 Step 4: OR multiply 40 cm by 30 cm = 1,200 cm2 then divide that number by 10,000 (100 cms x 100 cms in a metre squared) = 0.12 m2. Step 5: The correct answer is – c) 0.12 m2. a) 12m2 Refer to Explanation of Answer b) 1.2m2 Refer to Explanation of Answer c) 0.12m2 Correct Answer d) 0.012m2 Refer to Explanation of Answer None Question 39. Connor used Google maps to get directions to a friend’s house. The mobile device he was using showed the trip distance as 3000 metres. On the screen the trip distance measured 100 millimetres (0.1 metres). What was the scale of the map on Connor’s mobile device? Explanation of answer Step 1: Map scales are always presented as 1 : “something” which means a distance of one on the map is equal to a distance of “something” in reality. For example a map scale of 1 :10,000 means that 1 millimetre on the map equals 10,000 millimetres (10 metres) in reality. A map scale of 1 : 10,000 also means that 1 metre one the map equals 10,000 metres in reality. The units of measurement are not important as long as they are both the same on the map and in reality. Step 2: First we need to make the units in the question the same. In this instance we start working with the 0.1 metres because it has the same unit as the 3000 metres on the trip distance. Note that we cannot simply say that the map scale is 0.1 : 3000 as we must represent the scale with a 1 on the left hand side. Step 3: To make the 0.1 into a 1 we multiply it by 10. If we multiply the 0.1 by 10 we must also multiply the 3,000 by 10. Step 4: 0.1 x 10 = 1 and 3000 x 10 = 30,000 which means that a distance of 1 on the map is equal to 30,000 in reality. Step 5: The correct answer is – d) 1 :30,000 a) 1 : 30 Correct Answer b) 1 : 300 Refer to Explanation of Answer c) 1 : 3,000 Refer to Explanation of Answer d) 1 : 30,000 Refer to Explanation of Answer None Question 40. Isabella drove from Perth to Geraldton, an approximate distance of 450km. The trip lasted 6 hours. Select the statement that is correct. The average speed of Isabella’s trip was: Explanation of answer Step 1: The question asks which statement is correct. We need to go through each question to determine which one is incorrect. Step 2: 50 km per 30 mins: 30 mins x 12 = 6 hours so we need to multiply 50 km by 12 = 600km. This statement does not match the statement in the question. This statement is incorrect. Step 3: 75 km per 60 mins: 60 mins x 6 = 6 hours, so 75 km multiplied by 6 = 450 km. This statement is correct. Step 4: 170 km per 2 hours: 2 hrs x 3 = 6 hours, so 170 km multiplied by 3 = 510 km. This statement is incorrect. Step 5: 215 km per 3 hours: 3 hrs x 2 = 6 hours, so 215 km multiplied by 2 = 430 km. This statement is incorrect. Step 6: The correct answer is – b) 75km per 60 mins. a) 50 km per 30 mins Refer to Explanation of Answer b) 75 km per 60 mins Correct Answer c) 170 km per 2 hours Refer to Explanation of Answer d) 215 km per 3 hours Refer to Explanation of Answer None Question 41. The height of 7 players in an AFL team were measured and given below. 187, 191, 194, 198, 202, 202, 205 Their mean, median, mode and range were calculated. The recruitment manager selected two more players at the season draft with heights of 197 cm and 202 cm. For these select players, which of the following statements are true? Explanation of answer Step 1: If we add two more players’ statistics into the data range then we must see what impact they have on that data. Step 2: Mean (average): For the simple fact that we are adding different numbers (197 & 202) to the data range will change the average. In this case the new average becomes 197.56. (i.e. 187 + 191 + 194 + 197 + 198 + 202 + 202 + 202 + 205 divided by 9) This is the measurement that changes. Step 3: Median, which is also known as the middle number in the data set. In this case if we add 197 and 202 into the data range, 108 still remains the middle number. Step 4: Mode, which is also known as the most occurring number. This would stay the same as we now have 3 values of 202. Step 5: Range, which is simply the largest number minus the smallest number. This would stay the same as the first and last values did not change. Step 6: The correct answer is – a) The mean will change. a) The mean will change. Correct Answer b) The median will change. Refer to Explanation of Answer c) The mode will change. Refer to Explanation of Answer d) The range will change. Refer to Explanation of Answer None Question 42. Victoria Skype calls from Perth to Adelaide regularly for business. When it is 3:30pm in Adelaide, it is 1:00pm in Perth. Victoria had to make a Skype call at 1:15pm Adelaide time. What was the time in Perth when she had to make that Skype call? Explanation of answer Step 1: To determine when that Skype call was made we need to find the time difference between Perth and Adelaide. The hint is in the question. When it is 3:30pm in Adelaide it is 1:00pm in Perth. This means there is a 2 1⁄2 hour (2 hrs 30 mins) time difference between the two cities. Step 2: So when it is 1:15pm, Adelaide time, we must subtract 2 hrs and 30 mins off that time to get the Perth time. Take off 2 hours first – 1:15pm minus 2 hours = 11:15am. Step 3: Now take off 30 minutes from 11:15am = 10:45am. The time of the Skype call from Perth is 10:45am. Step 4: The correct answer is – b) 10:45am. a) 10:15am Refer to Explanation of Answer b) 10:45am Correct Answer c) 11:15am Refer to Explanation of Answer d) 11: 30am Refer to Explanation of Answer None Question 43. Lola wants to go on holiday to Bali. She saves 25% of her wage to pay for the holiday and is left with $1500 for other expenses. What is Lola’s wage? Explanation of answer Step 1: If Lola saves 25% and is left with $1,500, this means that the $1,500 makes up 75% of her wage. This represents 3⁄4 of her wage. The 25% represents 1⁄4 of her wage. Step 2: We need to break down the $1,500 into the other quarters to find out what the remaining 25% represents. So $1,500 broken down into the remaining 3⁄4 would be 1st 1⁄4 = $500, 2nd 1⁄4 = $500, 3rd 1⁄4 = $500. So the last 25% would have to be $500. Step 3: We need to add all those quarters together to get her final wage. 4 x $500 = $2,000. Step 4: The correct answer would be – c) $2,000. a) $1600 Refer to Explanation of Answer b) $1850 Refer to Explanation of Answer c) $2000 Correct Answer d) $2250 Refer to Explanation of Answer None Question 44. Daisy uses her measuring cups quite frequently when cooking. Their sizes are 1⁄2 cup, 1⁄4 cup, 1⁄3 cup, and 1⁄8 cup. What size is Daisy’s largest cup? Explanation of answer Step 1: The simple answer is that the smaller the denominator (bottom number) on the fraction the larger the size of the cup (or item that is being measured). Step 2: The correct answer is – d) 1⁄2 cup. a) 1⁄2 cup Correct Answer b) 1⁄4 cup Refer to Explanation of Answer c) 1⁄3 cup Refer to Explanation of Answer d) 1⁄8 cup Refer to Explanation of Answer None Question 45. An electronics store has a sale on during the month of September. The sale started on the 9th and finished on the 27th. How many days were the electronic items on sale for? Explanation of answer Step 1: The simple process to answer this question would be to use the visual stimulus (picture) to count how many days. Step 2: Do not simply subtract 9 from 27 as this will give you 18 days. You need to make sure you count the actual start and finish day of the sale. The sale was on for 19 days. Step 3: If a visual stimulus is not included then writing down each day to count the full days of the sale is advised. Step 4: The correct answer is – b) 19 days. a) 17 days Refer to Explanation of Answer b) 19 days Correct Answer c) 21 days Refer to Explanation of Answer d) 22 days Refer to Explanation of Answer None Question 46. At the bottom of a DVD cover this information is shown: The run time for the movie is approximately 172 minutes. The length of the movie is closest to: Select the statement that is true. Explanation of answer Step 1: This question requires a conversion from minutes to hours. There are 60 min per hour. For 2 hours it would be 120 mins, for 3 hours 180 mins. 0.5 of an hour is the same as 30 minutes. So 2.5 hours would be 120 mins + 30 mins = 150 mins. Step 2: Knowing that the movie runs for 172 minutes means that the movie is closest to 3 hours in run time. Step 3: The correct answer is – c) 3 hours. a) 2 hours Refer to Explanation of Answer b) 2.5 hours Refer to Explanation of Answer c) 3 hours Correct Answer d) 3.5 hours Refer to Explanation of Answer None Question 47. Jaylen has 4 bags of balloons, with 22 balloons in each packet. He wants to put the same number of balloons into 10 paper bags. What is the greatest number of balloons that Jaylen could put in each bag? Explanation of answer Step 1: This question requires you to find out how many balloons Jaylen has and then divide them into the paper bags equally. We need to multiply 4 bags of 22 balloons: 4 x 22 = 88 balloons. Step 2: To divide them up into the bags we need to divide 88 balloons between 10 bags. 88 ÷ 10 = 8.8 balloons per bag (you could also simply move the decimal point one place value to the left as you are dividing by 10). Step 3: You cannot give 8.8 balloons per bag so we round down to a whole number, which is 8. Step 4: The correct answer is – c) 8. a) 5 Refer to Explanation of Answer b) 6 Refer to Explanation of Answer c) 8 Correct Answer d) 10 Refer to Explanation of Answer None Question 48. Shane had to renovate his bathroom. He put a row of blue tiles at the bottom of the wall. Each tile was 5 centimetres in width. His wall was 5 metres in length, how many tiles did he use? Explanation of answer Step 1: You need to find out how many tiles there are in 1 metre. Each tile is 5 cm in width and we need to know how many fit into 100 cm (1 m). We need to divide 100 by 5 = 20 (to check we can multiply 20 by 5 = 100). Step 2: If there are 20 tiles in 1 m, then we times that by 5 to get the amount of tiles in 5 metres. Step 3: 20 tiles x 5 m = 100 tiles Step 4: The correct answer is – d) 100 tiles. a) 55 Refer to Explanation of Answer b) 80 Refer to Explanation of Answer c) 95 Refer to Explanation of Answer d) 100 Correct Answer None Question 49. David needs to cut a piece of aluminium into a circle for a welding job. The aluminium is in the shape of a rectangle. One side is 66 cm and the other is 44 cm. What is the radius of the largest circle David could cut? Explanation of answer Step 1: A circle can only be cut out of a rectangle when using the shortest side of the rectangle. We know that the shortest side of the rectangle is 44 cm. Step 2: We could get the diameter of the circle to touch each side of the metal sheet. In this case the diameter is 44 cm. However, the question asks for the radius of the circle. The radius is half of the diameter. Step 3: To get the radius we divide 44 cm by 2 = 22 cm. Step 4: The correct answer is – a) 22 cm. 22 cm Correct Answer 24 cm Refer to Explanation of Answer 32.5 cm Refer to Explanation of Answer 44 cm Refer to Explanation of Answer None Question 50. When Lola was is Bali she needed to exchange Australian (AUS) dollars to Indonesian Rupiahs (Rp). The exchange rate is: If Lola wants at least 1 million rupiahs for her holiday expenses, how many Australian dollars should she exchange? Explanation of answer Step 1: In the exchange rate box it says that 1 Australian dollar gets 10,300 Indonesian rupiahs. So exchanging $1 gets you Rp10 300. Step 2: If we exchange $10 we are adding a zero onto the Australian dollar, so all we need to do is add a zero onto the end of the exchanged rupiah = Rp103,000. Not quite one million. Step 3: If we exchange $100 we are adding two zeros onto the Australian dollar, then what we need to do is add two zeros onto the end of the exchanged rupiah = Rp1,030,000. This gives us one million and thirty thousand rupiah. So if Lola wants at least one million rupiah then she should exchange $100 Australian dollars. Step 4: The correct answer is – b) $100. a) $10 Refer to Explanation of Answer b) $100 Correct Answer c) $500 Refer to Explanation of Answer d) $1000 Refer to Explanation of Answer None Question 51. Shania is an active runner and runs regularly during the week. After one run she counted her pulse. She counted 12 beats in 5 seconds. What was her pulse rate in beats per minute (beats/min)? Explanation of answer Step 1: To get beats per min we must work with 60 seconds. As we are only given the information of 12 beats in 5 seconds we must multiply those numbers to get to 60 seconds. Step 2: Let’s start by doubling the beats and seconds. 12 x 2 = 24 beats and 5 x 2 = 10 seconds. 24 beats in 10 seconds. Step 3: We can now multiply 10 seconds by 6 to get 60 seconds: 6 x 10 = 60 seconds. Step 4: If we multiply 6 by 10 then we must multiply 24 by 6. To make it easier to calculate we should split up 24 into 20 and 4. 20 x 6 = 120, 4 x 6 = 24. 120 + 24 = 144. Shania’s pulse rate was 144 beats per minute after her run. Step 5: The correct answer is – d) 144 beats/min. a) 80 beats/min Refer to Explanation of Answer b) 96 beats/min Refer to Explanation of Answer c) 124 beats/min Refer to Explanation of Answer d) 144 beats/min Correct Answer None Question 52. Trent has to hire a car while his car is at the mechanic for a major service. He found this advertisement. Trent was told that these conditions apply: Daily rate of $35 (as per the advertisement) GPS optional at $15 per day. As Trent is 24 years of age, he must take out extra insurance. This is a one-off cost of $30. How much would it cost Trent to hire the car with the GPS for 5 days? Explanation of answer Step 1: First let’s start by figuring out how much it would cost Trent to hire the car for one day. $35 for the car and add $15 for the GPS = $50 day. Step 2: He is hiring the car for 5 days so 5 x $50 = $250. Step 3: He needs to pay the one-off insurance cost of $30 which we add to the $250. So $250 + $30 = $280. It costs Trent $280 dollars to hire the car for 5 days. Step 4: The correct answer is – d) $280. a) $205 Refer to Explanation of Answer b) $230 Refer to Explanation of Answer c) $255 Refer to Explanation of Answer d) $280 Correct Answer None Question 53. A house was for sale for $400,000. Three weeks later it was reduced by $40,000 Rhys bought the house for 1% less than the reduced price. How much did he pay for the house? Explanation of answer Step 1: You need to figure out what the reduced cost would be first. So $400,000 minus $40,000 = $360,000. Step 2: From there you need to figure out what 1% of $360 000 is. 1% of $100 = $1, 1% of $1000 = $10, 1% of $10,000 = $100, 1% of $100,000 = $1,000. So 1% of $360,000 = $3,600. Step 3: Then we must subtract $3,600 from $360,000. Subtracting $3,000 from $360,000 would be $357,000. Then subtract $600 from $357,000 = $356,400. So the price Rhys paid for the house was $356,400. Step 4: The correct answer is – c) $356,400. a) $352,000 Refer to Explanation of Answer b) $355,600 Refer to Explanation of Answer c) $356,400 Correct Answer d) $360,000 Refer to Explanation of Answer None Question 54. Maddy is building a model Lego house. She has adapted the base of the Lego mat to suit her building. What is the area of the Lego mat that she is going to build on? Explanation of Answer Step 1: First we have separated the three areas so we can easily calculate the total area. Step 2: The smaller areas at the bottom of the Lego mat are the easiest to work with. We need to use the two measurements (on the left hand side with the red and black numbers) to get the area. Multiply one red 10 cm by one black 5 cm. This is 10 cm x 5 cm = 50 cm2. Step 2: As the right hand side area is exactly the same measurement as the one on the left we know the area will be the same. This is 10 cm x 5 cm = 50 cm2. We now have 2 lots of 50 cm2. Step 3: The next section is the rectangle at the top of the Lego mat. We can see by separating the two areas we needed to recalculate the distances of this area. The height of the area becomes 10 cm (as shown in green) by subtracting 10 cm from the smaller area from the total distance of 20 cm. Step 3: The length is still 20 cm (as shown in black at the top of the Lego Mat). Step 4: To calculate the area of the larger rectangle we multiply 20 cm by 10 cm = 200 cm2. Step 5: Now we need to add all three areas together to get the final area. 200 cm2 + 50 cm2 + 50 cm2 = 300 cm2. Step 6: The correct answer is – b) 300 cm2. a) 250cm2 Refer to Explanation of Answer b) 300cm2 Correct Answer c) 400cm2 Refer to Explanation of Answer d) 500cm2 Refer to Explanation of Answer None Question 55. A pair of jeans was on sale with a 10% discount. Ellie received a further 10% off the already discounted price. If the original cost of the jeans cost $100, how much has she paid for the jeans? Explanation of answer Step 1: This question can be a trick question as you need to find 10% off the original price then 10% off the discounted price. Step 2: Find 10% of $100 = $10. Step 3: Subtract $10 from $100 = $90 (original discount price). Step 4: Find 10% of $90 = $9. Step 5: Subtract $9 from $90 = $81 (further 10% off price). Step 6: The final price for the jeans is therefore $81. Step 7: The correct answer is – c) $81. a) $79 Refer to Explanation of Answer b) $80 Refer to Explanation of Answer c) $81 Correct Answer d) $83 Refer to Explanation of Answer None Question 56. A morning breakfast news program started at 6:32am and ran for 148 minutes. What time did the show finish? Explanation of answer Step 1: This question requires you to manipulate minutes into hours so they we can find out the time the show finished. Step 2: There are 60 min per hour. For 2 hours it would be 120 mins, for 3 hours 180 mins. The show ran for 148 minutes. We know 2 hours = 120 minutes. So the show definitely ran over 2 hours. To find the remaining minutes we should subtract 120 mins from 148 mins. Step 3: 148 mins – 120 mins = 28 mins. Step 4: So the show went for 2 hours and 28 mins. We now need to add that amount of time to 6:32 to find the finishing time of the show. Step 5: 6:32 + 28 mins = 7:00am, add 2 hours = 9:00am. The show finished at 9:00am. Step 6: The correct answer is – d) 9:00am. a) 8:27am Refer to Explanation of Answer b) 8:41am Refer to Explanation of Answer c) 8:56am Refer to Explanation of Answer d) 9:00am Correct Answer None Question 57. A building and construction company is building a new stadium. They have estimated their costs to be: Materials $550,000,000 Labour $360,000,000 Planning fees $80,000,000 What is the estimated total cost, to the nearest $100,000,000? Explanation of answer Step 1: Don’t be overwhelmed with all the zeros in this question. You can remove them to do the simple maths first, and then return them to get a final answer. Step 2: The question asks us to round the estimated total to the nearest one hundred million dollars ($100,000,000). First we must add up the values to find the estimated total. Step 3: We can remove the 6 zeros after the totals to make is simpler to add those larger numbers. So $550 + $360 + $80 = $990. Now add the 6 zeros onto the total = $990,000,000. We have an estimate of nine hundred and ninety million dollars. Step 4: We need to round $990,000,000 to the nearest one hundred million dollars ($100,000,000). Step 5: Look at the number in the one hundred millions column, it is 9. Step 7: When rounding we need to look at the number on the right hand side of the number being rounded, in this case it is 9. Step 8: Because the 9 is closer to 10 we must round up the 9 in the one hundred millions column by 1 digit to 10. This gives us $1,000,000,000. Step 9: The correct answer is – b) $1,000,000,000. a) $990,000,000 Refer to Explanation of Answer b) $1,000,000,000 Correct Answer c) $1,010,000,000 Refer to Explanation of Answer d) $1,100,000,000 Refer to Explanation of Answer None Question 58. The predicted maximum and minimum temperatures for the next five days are shown below. What will be the average minimum temperature over the next 5 days? Explanation of answer Step 1: To find the average minimum temperature we would normally add all the minimum values together and divide that total by 5 (the number of values shown). 12 + 12 + 12 + 12 + 11 = 59. Divide 59 by 5 and we get 11.8° (50 ÷ 5 = 10, 9 ÷ 5 = 1.8, 10 + 1.8 = 11.8). Step 2: However, we do not have a calculator so we need to use a different method. We need to use the value between 11 and 12 degrees. The difference between 11° and 12° is 1°. If we divide 1° up into 5 equal parts then we get 0.2°. There are 4 values of 12° and one of 11°. We allocate 0.2° per each value of 12° (as this is the greater value than 11° and the average would be closer to 12°). Step 3: We add up each 0.2° (4 x 0.2) to get 0.8°. We add the 0.8° to 11° to get 11.8°. This would be the average minimum temperature over the 5 days. Step 4: The correct answer is – c) 11.8°. a) 11° Refer to Explanation of Answer b) 11.5° Refer to Explanation of Answer c) 11.8° Correct Answer d) 12° Refer to Explanation of Answer None Question 59. Max grew pumpkins in his backyard vegetable patch. When picking his pumpkins he noticed one was much heavier than the others. When he weighed the pumpkin it weighed 5.35 kilograms. The average of all the other pumpkins was 2.5 kilograms. How much heavier was the heavy pumpkin than the other pumpkins? Explanation of answer Step 1: To find the difference between the heavy pumpkin and the average weight of the other pumpkins we can manipulate the values slightly. Step 2: If we add 0.15 kg to 5.35 kg we have 5.5 kg. This is exactly 3 kg heavier than the averaged pumpkins. The answer is not 3 kg, because we have added 0.15 kg to that total. We need to subtract 0.15 kg from 3 kg to get 2.85 kg. This is the difference between the heavier pumpkin and the average weight of the other pumpkins. Step 3: The correct answer is – a) 2.85 kg. a) 2.85 kg Correct Answer b) 3.05 kg Refer to Explanation of Answer c) 3.15 kg Refer to Explanation of Answer d) 3.45 kg Refer to Explanation of Answer None Question 60. Luke was checking how much space he had on his computer before he tried to install a computer game on his hard drive. This is what he found: Movies: 325 GB Apps: 90 GB Audio: 75 GB Photo’s: 10 GB Free space ?? GB The size of Luke’s hard drive is 1 TB (terabyte). As a percentage, how much free space was available on Luke’s hard drive? Explanation of answer Step 1: First we must add all the items that are taking up space on his computer. We should try and match numbers together to make the addition easier. 325 GB + 75 GB = 400 GB, 90 GB + 10 GB = 100 GB. 400 GB + 100 GB = 500 GB. Step 2: The items on Luke’s computer take up 500 GB. This means he has 500 GB of free space on his hard drive. Step 3: The question asks that we represent his free space as a percentage. As Luke’s hard drive is 1 TB / 1,000 GB and he has 500 GB free, this means he is has exactly half (50%) of his hard drive as free space. Step 4: The correct answer is – c) 50%. a) 40% Refer to Explanation of Answer b) 45% Refer to Explanation of Answer c) 50% Correct Answer d) 55% Refer to Explanation of Answer None Question 61. It was half past three, 4 minutes ago. What is the time now? Explanation of answer: Step 1: First read the time in the first part of the question = 3:30. Step 2: The second part of the question states, 4 minutes ago. This means 4 minutes have passed since 3:30. Step 3: Add 4 minutes to 3:30 to get 3:34. Step 4: The correct answer is – c) 3:34 a) Refer to Explanation of Answer b) Refer to Explanation of Answer c) Correct Answer d) Refer to Explanation of Answer None Question 62. At what grid reference are the emus found? Explanation of answer: Step 1: When looking at the map you can either look for the emu symbol or the word emu. To help guide you to where the emus would be you can look under the Australian Bushwalk heading in orange. Step 2: The emus are found in grid reference C4. Step 3: The correct answer is – d) C4 a) B3 Refer to Explanation of Answer b) D4 Refer to Explanation of Answer c) E9 Refer to Explanation of Answer d) C4 Correct Answer None Question 63. After visiting the emus, I walk to the rhinoceros enclosure. In what direction did I walk? Explanation of answer: Step 1: To answer this question you must find the compass on the map. It is located in the top left hand corner of the map underneath the Key. Look for the direction of North and determine the other directions. Step 2: Find the emus and the rhinoceroses on the map. Use the compass to help you find the direction of that travel from the emus to the rhinoceroses. Step 3: You should be travelling in a Southerly (S) direction. Step 4: The correct answer is – b) S a) SE Refer to Explanation of Answer b) S Correct Answer c) E Refer to Explanation of Answer d) SW Refer to Explanation of Answer None Question 64. The Mandurah region has 32 registered Uber cars and drivers. Of the 32 cars, ½ are Holdens, ¼ are Fords and the rest are Toyotas. How many cars are Toyotas? Explanation of answer: Step 1: To find out how many Toyotas there are, we must find out how many Holdens and Fords are being used for Uber. Step 2: Of the 32 cars, ½ are Holden. Divide 32 by 2 to get 16cars. This is the same as multiplying 32 by ½. Step 3: Of the 32 cars ¼ are Fords. Divide 32 by 4 to get 8 cars. This is the same as multiplying 32 by ¼. Alternatively you could divide 32 by 2 to get 16, and then divide 16 by 2 to get 8 cars. This is the same as multiplying 32 by ½ and then by ½ again (32 x ½ x ½ = 32 x ¼ = 32 ÷ 4 = 8). Step 4: If you have 32 cars total and 16 are Holdens and 8 are Fords we can subtract those totals from 32 to get the number of Toyotas. 32 – 16 = 16, 16 – 8 = 8. We have 8 cars that are Toyotas. Step 5: The correct answer is – b) 8 Alternative explanation: Step 1: A half is the same as two quarters. If half the cars are Holdens and one quarter are Fords, then in total, three quarters of all the Uber cars are not Toyotas. Step 2: Since “the rest are Toyotas”, that means that one quarter of all of the cars are Toyotas. Four quarters minus three quarters leaves one quarter. Step 3: All we have to work out is how many cars one quarter of 32 is. Divide 32 by 4 to get 8 cars. This is the same as multiplying 32 by ¼. Alternatively you could divide 32 by 2 to get 16, and then divide 16 by 2 to get 8 cars. This is the same as multiplying 32 by ½ and then by ½ again (32 x ½ x ½ = 32 x ¼ = 32 ÷ 4 = 8) Step 4: The correct answer is – b) 8 a) 6 Refer to Explanation of Answer b) 8 Correct Answer c) 12 Refer to Explanation of Answer d) 16 Refer to Explanation of Answer None Question 65. The birthdates of four friends are below: Explanation of answer: Step 1: As all the dates are presented in different format, we need to look at what common numbers are the same and then find the points of difference. Firstly, look at the year they were all born: 1975, this year is the same for all friends. We can’t determine who is the youngest from this info. Step 2: Next we should look at the months. These are different, two are in number form and two are in word form. If we place them in month order; 03 is March, then April, then May then 06, which is June. We can now find out who is the youngest from this info. Step 3: Anyone born in March, April or May would be older than someone born in June, so the person who is the youngest in this group of friends would be the one born in June. This is John. Step 4: The correct answer is – d) John a) Peter Refer to Explanation of Answer b) Bruce Refer to Explanation of Answer c) Phillip Refer to Explanation of Answer d) John Correct Answer None Question 66. This graph shows the average daily power usage of a family home over 2 years. Explanation of answer: Step 1: To answer this question you must compare the data from each season in 2014 to the same season in 2015 and find the approximate difference between the two. For example summer 2014 had 800 kWh usage and summer 2015 had about 780 kWh usage, which equals a 20 kW difference. We need to do that for each season to find the answer. Step 2: Autumn 2014 = 550 kW, Autumn 2015 = 530 kW = Difference of 20 kW Step 3: Winter 2014 = 700 kW, Winter 2015 = 750 kW = Difference of 50 kW Step 4: Spring 2014 = 600 kW, Spring 2015 = 580 kW = Difference of 20 kW Step 5: The season with the largest difference in power usage is Winter Step 6: The correct answer is – c) Winter a) Summer Refer to Explanation of Answer b) Autumn Refer to Explanation of Answer c) Winter Correct Answer d) Spring Refer to Explanation of Answer None Question 67. At the end of the trading day a newsagency has a number of notes in the till. They are: a) What was the amount collected in notes? Please select your answer a) $385 [reason] Refer to Explanation of Answer b) $400 Refer to Explanation of Answer c) $435 Correct Answer d) $460 Refer to Explanation of Answer b) $43.75 was collected in coins; in total how much was collected altogether? Please select your answer a) $475.75 Refer to Explanation of Answer b) $476.75 Refer to Explanation of Answer c) $477.75 Refer to Explanation of Answer d) $478.75 Correct Answer Explanation of answer: Step 1: To find out the answer for a) you must find out the totals of all the notes. 2 x $100 = $200, 3 x $50 = $150, 1 x $20 = $20, 4 x $10 = $40, 5 x $5 = $25. Step 2: Then add them together: $200 + $150 + $20 + $40 + $25 = $435. This gives you the answer for a) Step 3: Now that you know the amount for notes, you can add the coins to the notes to get the answer for b). This is: $435 + $43.75 = $478.75. This is the answer for b) Question 68. Mark filled up 5 buckets of water and weighed each one. He wrote the weight on each bucket. If he goes to pick up the two heaviest buckets how many kilograms would he be holding in total? Explanation of answer: Step 1: To answer this question you must know decimal places and the place value of each number. The closer the number to the decimal place (on the right hand of the decimal place) the larger the value of the number. For example 0.2 is ten times larger than 0.02. We have to look for the two largest values to add together. Step 2: The find the two heaviest buckets, we must find the two buckets that add to the largest value. For example: 8.2 kg + 8.032 kg = 16.232 kg, which is answer d) Step 3: 8.2 kg + 8.302 kg = 16.502kg, which is answer c) Step 4: 8.2 kg + 8.32 kg = 16.520 kg, which is answer b) Step 5: 8.302 kg + 8.32 kg = 16.622kg, which is answer a) Step 6: The correct answer is – a) 16.622 kg Alternative explanation: Step 1: Arranging the four different weights top to bottom from largest to smallest we get: 8.320 – largest 8.302 8.200 8.032 8.020 – smallest Step 2: We are only interested in the two largest weights, 8.32kg and 8.302kg. Adding these together gives us 8.32 kg + 8.302 kg = 16.622kg, which is answer a). Step 3: The correct answer is – a) 16.622 kg a) 16.622 kg Correct Answer b) 16.520 kg Refer to Explanation of Answer c) 16.502 kg Refer to Explanation of Answer d) 16.232 kg Refer to Explanation of Answer None Question 69. You have 4 Masters Choc milk containers. Each has 600 mL of Choc milk in them. You are sharing the Choc milk with 5 friends. You have five 450 mL glasses to share the milk with. How much milk would you have left over after filling those 5 glasses? Explanation of answer: Step 1: Figure out how much Choc milk we have first. Four containers with 600 mL each means 4 x 600 mL = 2,400 mL Step 2: Figure out how much milk needs to be shared. Five glasses that hold 450 mL each means 5 x 450 mL. Let’s break down that sum. 5 x 400 mL = 2,000 mL, 5 x 50 mL = 250 mL. 2,000 mL + 250 mL = 2,250 mL. Step 3: Find the difference between 2,400 mL and 2,250 mL = 2,400 mL – 2,250 mL = 150 mL Step 4: We have 150 mL of the Choc milk left over. Step 5: The correct answer is – c) 150 mL a) 50 mL Refer to Explanation of Answer b) 100 mL Refer to Explanation of Answer c) 150 mL Correct Answer d) 200 mL Refer to Explanation of Answer None Question 70. A runner is starting to train for a long distance event. The runner runs a 5.6 km course 4 times a week and also runs on the weekend. The total distance for the week is 35 km. What is the distance run on the weekend? Explanation of answer: Step 1: To find out the total distance run on the weekend we must first find out how many kilometres they have run during the week. That person ran 5.6 km, 4 times a week. So 4 x 5 km = 20 km and 4 x 0.6 km = 2.4 km. 20 km + 2.4 km = 22.4 km. Step 2: Now that we know they ran 22.4 km during the week we can subtract that total from 35 km to give us the distance run on the weekend. 35 km – 22.4 km = 12.6 km. Step 3: Alternatively we can do it this way: 30 km – 20 km = 10km. 5 km – 2.4 km = 2.6 km. 10 km + 2.6 km = 12.6 km. Step 4: They ran 12.6 km on the weekend. Step 5: The correct answer is – b) 12.6 km a) 14.3 km Refer to Explanation of Answer b) 12.6 km Correct Answer c) 10.9 km Refer to Explanation of Answer d) 8.9 km Refer to Explanation of Answer None Question 71. A group of 30 AFL supporters are organising a catch up to watch an AFL match. Sixteen are Richmond supporters. The remaining people are Western Bulldogs supporters. One person is allocated to organise the catch up. What is the probability that a Richmond supporter will be allocated to organise the catch up? Explanation of answer: Step 1: To answer this question we must first figure out how many Richmond supporters there are in relation to the group. There are 16 Richmond supporters out of the 30 group members. This means there are 16⁄30 Richmond supporters. Step 2: The next part of the question asks us what is the probability that a Richmond supporter will be picked from the group. As we know there are 16⁄30 Richmond supporters in the group. The probability would be 16⁄30. Step 3: Be careful when picking the answer, as there is another correct answer in the multiple choice answers. 8⁄15 would also be correct as 8⁄15 is exactly the same as 16⁄30. The reason being is that 8⁄15 is the simplified version of 16⁄30. The numerator and denominator have both been divided by 2 to give the simplified answer of 8⁄15. Step 4: The correct answers are – a) 16⁄30 AND c) 8⁄15 a) 16⁄30 Correct Answer b) 1⁄16 Refer to Explanation of Answer c) 8⁄15 Correct Answer d) 14⁄30 Refer to Explanation of Answer Question 72. The table below shows the height, in metres, of the tides at Derby for five days in December 2016. Low tides are printed in red and high tides are printed in blue. What was the difference between the highest and the lowest tides on Saturday, 3rd of December? Explanation of answer: Step 1: In the table look for the row Saturday 3rd of December. Scan across and look for the red and blue digits. The tide height is under the coloured digits. The arrow pointing up is the high tide and the arrow pointing down is the low tide. Step 2: To find the difference between the high and low tides we must find the largest high tide and smallest low tide. The largest high tide is 9.3 m and the smallest low tide is 0.5m. Step 3: 9.3 m subtract 0.5 m is 8.8 m, the difference between the highest and lowest tide is 8.8 m Step 4: The correct answer is – a) 8.8 m a) 8.8 m Correct Answer b) 7.3 m Refer to Explanation of Answer c) 11.1 m Refer to Explanation of Answer d) 9.8 m Refer to Explanation of Answer None Question 73. The shape of a market garden paddock is a rectangle. It is 1.8 kilometres long and 700 metres wide. There is a fence around the entire paddock What is the length of the fence? Explanation of answer: Step 1: To answer this question you need to figure out the length of the fencing and to understand what a rectangle is. A rectangle has two sides, which in this case are 1.8 km long and two sides which are 700 m long. Step 2: Convert the 700 m to kilometres. 700 m = 0.7 km. This makes is easier to add the totals when they are all in the same unit of length. Step 3: The total length is (1.8 km x 2) + (0.7 km x 2) = (3.6 km + 1.4 km) = 5.0 km. Step 4: The correct answer is – c) 5.0 km a) 3.8 km Refer to Explanation of Answer b) 4.6 km Refer to Explanation of Answer c) 5.0 km Correct Answer d) 5.4 km Refer to Explanation of Answer None Question 74. An oven dial displays the temperature in degrees Celsius. The temperature shown on the dial above is closest to: Explanation of answer: Step 1: As the dial shows a dot to signal the temperature you will need to estimate the approximate temperature. In this case the dot is close to 220°C to about 225°C. Step 2: By looking at the answers provided in the multiple choice section the only answer that is close to our estimation is c) 225°C. Step 3: The correct answer is – c) 225°C a) 200°C Refer to Explanation of Answer b) 210°C Refer to Explanation of Answer c) 225°C Correct Answer d) 240°C Refer to Explanation of Answer None Question 75. A swimming pool has a length of 50 metres. The shallow end has a depth of 1.5 m and the deep end has a maximum depth of 4 m. There is a gradual slope from the shallow end to the deep end. Which diagram shows the correct profile of a side wall of the pool? Explanation of answer: Step 1: Since none of the images a) to d) are to scale or dimensioned, the length and depths stated in the question are irrelevant. The diagram that we are looking for must have three components; a deep end, a shallow end, and a gradual slope between the two. The diagram best suiting this description is answer c). Step 2: The correct answer is – c) a) Refer to Explanation of Answer b) Refer to Explanation of Answer c) Correct Answer d) Refer to Explanation of Answer None Question 76. Scott buys biscuits and savoury rolls for a morning tea. He buys 20 biscuits at $2 each and 20 savoury rolls at $3 each. Select all of the expressions that show the amount that Scott should pay in dollars. Explanation of answer: Step 1: To complete this answer you must use the order of operations acronym BIMDAS (brackets, indices, multiplication, division, addition and subtraction) in that order. Step 2: Before we use BIMDAS we must figure out how much it costs Scott to buy both the biscuits and rolls. The biscuits cost $2 x 20 = $40. The rolls cost $3 x 20 = $60. The total cost would be $40 + $60 = $100. Step 3: Looking at the answers given we would do the multiplication first then addition. Let’s go through each answer. Step 4: a) 2 + 3 x 20: 3 x 20 = 60, then 2 + 60 = $62. Not the correct answer. Step 5: b) 20 x 2 + 3: 20 x 2 = 40, then 40 + 3 = 43 = $43. Not the correct answer. Step 6: c) 20 x 2 + 20 x 3: 20 x 2: = 40, then 20 x 3 = 60 then, 40 + 60 = $100. The correct answer. Step 7: d) 5 x 20: 5 x 20 = 100 = $100. The correct answer. Step 8: The correct answer is – both c) 20 x 2 + 20 x 3 AND d) 5 x 20 a) 2 + 3 x 20 Refer to Explanation of Answer b) 20 x 2 + 3 Refer to Explanation of Answer c) 20 x 2 + 20 x 3 Correct Answer d) 5 x 20 Correct Answer Question 77. Ethan wanted to estimate the length of a block of land. He counted 71 paces. Each pace was about 65 centimetres. The length of the block is closest to: Explanation of answer: Step 1: To answer this question we could simply multiply 71 by 65 to get our answer on a calculator, however, we don’t have one so we need to break down the numbers into parts. Step 2: Let’s break the 71 paces into two parts; 70 and 1. Step 3: Break down the 65 cms into two parts; 60 cms and 5 cms Step 4: We need to break down these numbers so we can work with different units of place value. This will allow us to do this calculation without a calculator. Step 5: Multiply 70 by 60 cms = 4,200 cms (7 x 6 = 42, then add two 0’s on the end to get 4,200 cms) Step 6: Multiply 70 by 5 cms = 350 cms (7 x 5 = 35, then add one 0 on the end to get 350 cms) Step 7: Multiply 65 by 1 = 65 cms Step 8: Add all the totals together; 4,200 + 350 + 65 = 4,615 cms Step 9: The answer we have is in centimetres; however, we need to the answer in metres. To do this we divide 4,615cm by 100 (100 cms in one metre), this gives us 46.15 m Step 10: The answer of 46.15 m is closest to the multiple choice answer of d) 46 m Step 11: The correct answer is – d) 46 m a) 42 m Refer to Explanation of Answer b) 44 m Refer to Explanation of Answer c) 45 m Refer to Explanation of Answer d) 46 m Correct Answer None Question 78. The graph below compares the times of trains that run to Fremantle Station and their arrival schedule. What percentage of the trains were early? Explanation of answer: Step 1: To determine what percentage of the trains were early we should look at some of the other arrival times to see what their percentages would be. Step 2: If we look at the “On time” section of the graph this would constitute about half of the graph which would equal about 50% of the time the train arrives “On time”. If we look at the “Late” section of the graph this would constitute about a quarter of the graph which would equal about 25% of the time the train arrives “Late”. Step 3: When looking at the “Early” section, that section is smaller that the “Late” section, so it must be less than 25% of the time. Step 4: When looking at the multiple choice answers the best answer would have to be c) Between 10% and 25% based on the size of that section in the pie graph. Step 5: The correct answer is – c) Between 10% and 25% a) About 50% Refer to Explanation of Answer b) Between 25% and 33% Refer to Explanation of Answer c) Between 10% and 25% Correct Answer d) Less than 10% Refer to Explanation of Answer None Question 79. A bank pays 1.25% simple interest per year on a term deposit If you deposit $5,000 into that term deposit for 1 year, how much interest should the bank pay out? Explanation of answer: Step 1: The way to answer this question is to determine what 1% of $5,000. 10% would be $500, so 1% would be $50. Step 2: To find out what 0.25% would be, we need to understand what that represents as a fraction, which is ¼ or one quarter. To find out what ¼ of 1% is, we halve the original number ($50 ÷ 2 = $25), then halve that number again ($25 ÷ 2 = $12.50). We now have one quarter or 0.25% of 1%, which is $12.50. Step 3: To find out how much 1.25% of $5,000 is we add the 1% ($50) and the 0.25% ($12.50) together to get ($50 + $12.50 = $62.50) the answer of d) $62.50 Step 4: The correct answer is – d) $62.50 a) $50 Refer to Explanation of Answer b) $55 Refer to Explanation of Answer c) $60 Refer to Explanation of Answer d) $62.50 Correct Answer None Question 80. Rose and her four friends went out for lunch. The total bill for the lunch was $67.20. Rose was the only one to have a cup of coffee. She paid $4 for her coffee and the rest of the bill was shared equally. Which expression shows the total amount of money Rose paid for her lunch? Complete correctly: The total amount Rose paid for her lunch is equal to: Please select your answer a) (67.20 – 4) ÷ 5 Refer to Explanation of Answer b) (67.20 + 4) ÷ 5 Refer to Explanation of Answer c) (67.20 + 4) ÷ 5 - 4 Refer to Explanation of Answer d) (67.20 – 4) ÷ 5 + 4 Correct Answer Explanation of answer: Step 1: To complete this answer you must use the order of operations acronym BIMDAS (brackets, indices, multiplication, division, addition and subtraction) step by step to find the answer. We do not need to know the value amount of the meal and coffee only the expression which would lead us to the final cost. Step 2: To figure out how much it costs Rose for her meal we must break the bill into sections. If the total bill costs $67.20, we must subtract $4 from it to determine the portion that is to be shared. This is the first step and is represented by (67.2 – 4). Step 3: The next step requires use to divide the shared portion between the 5 friends. This would be represented by ÷ 5 in the equation. Step 4: The next step would be add the value of the coffee back onto Rose’s amount. This would be represented by + 4 in the equation. Step 5: We add all the components together to give the final equation of: (67.20 – 4) ÷ 5 + 4 Step 6: The correct answer is – d) (67.20 – 4) ÷ 5 + 4. Question 81. Four university students are renting a house. They all share an equal part of the rent. They each pay $120 per week. Two more students will move into the house and the rent will be shared equally between all six people. By how much does the weekly rent per student decrease? Explanation of answer: Step 1: First we need to find out the total amount of rent that is being paid by the students. This would be 4 students times $120 each. 4 x $120 = $480. Step 2: If there are now 6 students renting the house, we would divide $480 by 6 students to figure out how much each would pay. $480 ÷ 6 = $80 (6 times tables = 6 x 8 = 48). Step 3: Now we have to figure out the difference between the totals. $120 – $80 = $40. Step 4: The rent decreases by $40 per student. Step 5: The correct answer is – a) $40 a) $40 Correct Answer b) $45 Refer to Explanation of Answer c) $50 Refer to Explanation of Answer d) $60 Refer to Explanation of Answer None Question 82. Georgie completed a training run in 30 minutes. She ran at a steady speed of 8 km/h. The distance of the run is equal to: Explanation of answer: Step 1: 30 minutes is exactly half of 60 minutes, and is therefore half an hour. Step 2: If she was running at a steady pace of 8 km/h and ran for half an hour, then she would only have had enough time to run half of 8 kilometres. Therefore, she ran 4 kilometres. Step 3: The correct answer is – b) 4 km a) 3.5 km Refer to Explanation of Answer b) 4 km Correct Answer c) 4.5 km Refer to Explanation of Answer d) 5 km Refer to Explanation of Answer None Question 83. A home security system takes an image every 10 seconds. Each image is deleted 20 hours after it was taken. What is the largest number of images that can be stored in the camera? Explanation of answer: Step 1: Use the first piece of information that is given to us. We have an image every 10 seconds. This means there are 6 images every minute. There would be 12 images in 2 minutes, 30 images in 5 minutes, 60 images in 10 minutes and 360 images in 1 hour: (6 x 60 = 6 x 6 x 10 = 36 x 10 = 360). Step 2: If there are 360 images in 1 hour there would be 3,600 in 10 hours (360 x 10 = 3,600). If 10 hours gives us 3,600 images then we should multiply 3,600 by 2 to give us 20 hours worth of images (10 x 2 = 20 hours and 3,600 x 2 = 7,200 images). Step 3: This means over 20 hours the camera has taken 7,200 images. Step 4: The correct answer is – c) 7,200 images. a) 6,000 images Refer to Explanation of Answer b) 6,900 images Refer to Explanation of Answer c) 7,200 images Correct Answer d) 7,600 images Refer to Explanation of Answer None Question 84. Julia works 38 hours a week as a secretary and earns $22 per hour. Every fortnight, $340 of tax is taken from her pay. How much pay does Julia take home each fortnight? Explanation of answer: Step 1: First we must figure out what Julia’s total pay would be for one week. This requires us to multiply 38 by 22. To do this, multiply 38 by 10 to give $380. Then multiply 380 by 2 (same as 38 x 20) = $760. Then we must multiply 38 by 2 (we left 2 off the 22 at the start). 38 x 2 = $76. Then add $760 and $76 = $836. Step 2: Julia’s pay for one week is $836, to figure out how much she gets paid for a fortnight we must multiply that by 2 (2 weeks in a fortnight). $836 x 2 = $1,672 (800 x 2 = 1,600, 30 x 2 = 60, 6 x 2 = 12, then 800 + 60 + 12 = 1,672). Julia earns $1,672 per fortnight. Step 3: She is taxed $340 per fortnight, we must subtract this from $1,672. Let’s subtract $300 from $1,672. $1,672 – $300 = $1,372. Now take $40 from $1,372. $1,372 – $40 = $1,332. Julia takes home $1,332 per fortnight after tax. Step 4: The correct answer is – b) $1,332. a) $1,287 Refer to Explanation of Answer b) $1,332 Correct Answer c) $1,372 Refer to Explanation of Answer d) $1,408 Refer to Explanation of Answer None Question 85. A 10 kilometre section of highway is to be resurfaced. The highway is straight and is 6.3 metres wide. How many square metres of the road need to be resurfaced? Please select your answer a) 13,000 m<sup>2</sup> Refer to Explanation of Answer b) 47,000 m<sup>2</sup> Refer to Explanation of Answer c) 63,000 m<sup>2</sup> Correct Answer d) 87,000 m<sup>2</sup> Refer to Explanation of Answer Explanation of answer: Step 1: To find the answer in metres squared we must convert the 10 km to metres. As there is 1000 metres in a kilometre, there must be 10,000 metres in 10 km. Step 2: Next we must multiply 6.3 metres by 10,000 metres (10 km) to get the total square metres. 6.3 x 10,000 = 63,000 m2 Step 3: There needs to be 63,000 m2 of road resurfaced. Step 4: The correct answer is – c) 63,000 m2 Question 86. To supplement his diet, Campbell takes 500 milligrams of calcium every day. So far, he has taken a total of 25 grams. Approximately for how long has Campbell been taking calcium? Explanation of answer: Step 1: First we must know how many milligrams in a gram to work this problem out. There are 1,000 milligrams in 1 gram. This means that 500 milligrams are ½ (0.5) a gram. Step 2: This means that Campbell needs to take 2 tablets to take 1 gram of calcium. This also means that if he takes 500 milligrams per day it takes 2 days to take 1 gram of calcium. Step 3: So if he has taken a total of 25 grams, we double it to find out how many days he has been taking calcium. 25 x 2 = 50 days. Campbell has been taking calcium for 50 days. Step 4: The correct answer is – d) 50 days. a) 25 days Refer to Explanation of Answer b) 35 days Refer to Explanation of Answer c) 43 days Refer to Explanation of Answer d) 50 days Correct Answer None Question 87. You can buy soft drink from a shop in different ways. One 2 litre bottle will cost you $3.00 Two smaller 1.25 litre bottles for a total for $5 A box of twenty 350 millilitre cans for $16 When comparing the cost per litre, what is the correct order from the lowest to highest cost per litre? Explanation of answer: Step 1: To figure out the cost per litre we must divide the cost by the amount of litres. For the 2 litre bottle we divide $3 by 2 litres = $1.5 per litre. Step 2: For the 2 smaller 1.25 litre bottles, we divide $5 by 2.5 litres (2 x 1.25L) = $2 per litre. Step 3: For the cans we must figure out how many litres we have if we have 20 cans, but let’s start by multiplying by 10 cans. 350 x 10 = 3,500 millilitres or 3.5 litres, now times that by 2 to get 20 cans. 3.5 litres x 2 = 7 litres. Now we divide $16 by 7 litres = approximately $2.3 per litre ($14 ÷ 7 = $2, $2 ÷ 7 = approx $0.3, $2 + $0.3 = $2.3). Step 4: This means that the correct order from lowest cost to highest cost per litre is: One 2 litre bottle, two smaller bottles and a box of cans. Step 5: The correct answer is – c) One 2 litre bottle, two smaller bottles and a box of cans. a) Two smaller bottles, one 2 litre bottle, a box of cans. Refer to Explanation of Answer b) A box of cans, one 2 litre bottle, two smaller bottles. Refer to Explanation of Answer c) One 2 litre bottle, two smaller bottles, a box of cans. Correct Answer d) Two smaller bottles, a box of cans, one 2 litre bottle. Refer to Explanation of Answer None Question 88. Gavin uses a diagram, with a scale of 1:10, to calculate the area of his bathroom. If the diagram is 20 cm long and 15 cm wide, what is the area of Gavin’s actual bathroom? Explanation of answer: Step 1: The scale in this question means that if you have 1 cm on the diagram it equals 10 cms in real life. So in this instance, the length of the diagram is 20 cms long. We need to multiply that by 10 to find out the real length of the bathroom. 20 x 10 = 200 cms. 200 cms is the same as 2 metres. Step 2: The width of diagram is 15 cm wide. We need to multiply that by 10 to find out the real width of the bathroom. 15 x 10 = 150 cms. 150 cms is the same as 1.5 metres. Step 3: We multiply the 2 metres by 1.5 metres to get the area. 2 m x 1.5 m = 3 m2. The bathroom is 3 m2 in real life. Step 4: The correct answer is – d) 3 m2. a) 20 m2 Refer to Explanation of Answer b) 12.5 m2 Refer to Explanation of Answer c) 6 m2 Refer to Explanation of Answer d) 3 m2 Correct Answer None Question 89. A standard paperclip weighs 1 gram. I collected one hundred thousand paperclips. I wanted to estimate the mass of the collection in grams. Which statement does not reflect this estimation? Explanation of answer: Step 1: The question asks you to estimate the mass of the collection of paperclips in grams. If 1 paperclip weighs 1 gram then 100,000 paperclips will weigh 100,000 grams. So we are looking for the statement that does not have an answer of 100,000. Step 2: statement a) 50 x 2,000 = 100,000. A correct answer. Step 3: statement b) 100,000 ÷ 1000 = 100. Not a correct answer. Step 4: statement c) 100 x 1,000 = 100,000. A correct answer. Step 5: statement d) 10 x 10,000 = 100,000. A correct answer. Step 6: The correct answer is – b) Counting the number of paperclips in 1 kilogram, then dividing 100,000 by this number. a) Finding the mass of 50 paperclips, then multiplying by 2,000 Refer to Explanation of Answer b) Counting the number of paperclips in 1 kilogram, then dividing 100,000 by this number. Correct Answer c) Finding the mass of 100 paperclips, then multiplying by 1,000. Refer to Explanation of Answer d) Counting the paperclips in groups of 10, then multiplying the number of groups by 10,000. Refer to Explanation of Answer None Question 90. Noah wants to save for a new motorbike. He spends 75% of his wage and is left with $300 to save per week for the motorbike. Explanation of answer: Step 1: If Noah spends 75% and is left with $300, this means that the $300 makes up 25% of his wage. This represents ¼ of his wage. The 75% represents ¾ of his wage. Step 2: If $300 represents ¼ of his wage then we can multiply $300 by 4 to get his total wage (4 quarters make a whole).4 x $300 = $1,200. Step 3: Noah’s wage per week is $1,200. Step 4: The correct answer is – d) $1,200. a) $600 Refer to Explanation of Answer b) $800 Refer to Explanation of Answer c) $1,000 Refer to Explanation of Answer d) $1,200 Correct Answer None Question 91. In a game, two standard dice are thrown. The numbers that are facing up are added together. That number will determine how many spaces a player moves. If Ethan throws a 6 or 7 on his turn, he would land on a yellow square. What is the probability that Ethan would land on a yellow square? Explanation of answer: Step 1: When rolling a single dice, the probability of rolling a particular value are 1⁄6. There is an equal probability of rolling each of the numbers 1 – 6 because the dice is a cube which has six faces. But when we have two dice the probability of rolling a particular number is not as simple. For example, there’s only one way to roll a two (1+1), but there’s a lot of ways to roll a seven (1+6, 2+5, 3+4, 4+3, 5+2 and 6+1). Also, since each dice has 6 faces, there are 6 x 6 = 36 possible combinations of dice faces that could land facing up. Step 2: There are 5 possible ways to roll a 6 (1+5, 2+4, 3+3, 4+2 and 5+1). There are 6 possible ways to roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2 and 6+1). This gives us a total of 11 (5 + 6) distinct possible ways of rolling either a 6 or a 7. Step 3: The probability of Ethan landing on a yellow square is therefore 11⁄36 i.e. 11 possible ways of rolling a 6 or a 7 out of 36 possible dice face combinations. Step 4: The correct answer is – d)11⁄36 2⁄36 Refer to Explanation of Answer 6⁄36 Refer to Explanation of Answer 9⁄36 Refer to Explanation of Answer 11⁄36 Correct Answer None Question 92. A plane flight left from Melbourne to Perth. The time of departure in Melbourne was 10:00 and the flight arrived in Perth at 14:00. Melbourne time is 2 hours ahead of Perth time. If the distance flown was 2,720 kilometres, what was the approximate average flying speed of the plane? Explanation of answer: Step 1: There is some important information in this question. We need to know that Melbourne time is 2 hours ahead of Perth time. If the flight left at 10:00 and landed at 14:00, it took 4 hours flying time, but we must add 2 hours because of the time difference between each city. 6 hours is the number we have to work with. Alternatively, we can consider only the time in Perth. When the plane took off in Melbourne, the time in Perth would have been 8:00 because Perth is 2 hours behind Melbourne. When the plane landed, the time in Perth was 14:00. The difference in time between 8:00 and 14:00 is 6 hours, which is the actual amount of time that the plane was in the air. Step 2: To find the average flying speed of the plane we need to divide the total distance by the flying time. This means 2,720 km ÷ 6 = ? Step 3: Break down 2,720 km into 2,400 km and 320 km. Divide 2,400 km by 6 = 400 km. Divide 320 km by 6 ≈ 53 km. 400 km + 53 km = 453 km. This means the plane will cover approximately 453 km in 1 hour. This is the approximate average speed of the plane = 453 km/h. Step 4: The correct answer is – b) 453 km/h. a) 398 km/h Refer to Explanation of Answer b) 453 km/h Correct Answer c) 512 km/h Refer to Explanation of Answer d) 576 km/h Refer to Explanation of Answer None Question 93. A bobcat driver has to estimate the volume, V, of sand in a pile for removal. The pile forms a cone shape, 4 metres across the base and 1.5 metres high. Using the formula in the box, which of these answers is the best estimate of the volume of the sand pile? Explanation of answer: Step 1: To complete this answer you must use the order of operations acronym BIMDAS (brackets, indices, multiplication, division, addition and subtraction) in that order. We will answer this question line by line to get the answer. Step 2: V = 1⁄3(π r2) h. Step 3: V = 1⁄3(3.14 x 22) h : The radius is half the length of the base, in this case 2 is half of 4. The value of π is rounded to 3.14. Step 4: V = 1⁄3(3.14 x 4) h : 22is the same as 2 x 2 = 4. Step 5: V = 1⁄3(12) h : 3.14 x 4 = 12 (we round the value of 3.14 to 3 as we are estimating). Step 6: V = (1⁄3 x 12) h : we now do 1⁄3 x 12 = 4 Step 7: V = 4 x h : The height is 1.5, so we multiply 4 by 1.5 = 6 Step 8: V = 4 x 1.5 = 6 Step 9: V = 6 m3 Step 10: The correct answer is – d) 6 m3 a) 35 m3 Refer to Explanation of Answer b) 21 m3 Refer to Explanation of Answer c) 13 m3 Refer to Explanation of Answer d) 6 m3 Correct Answer None Question 94. A rectangular prism is cut in half and forms two cubes. The original prism had 6 faces and 12 edges. How many faces do the two cubes have combined? Explanation of answer: Step 1: The best way to explain how the rectangular prism becomes two cubes is to show a diagram of those two cubes. Step 2: The two cubes look like this: Step 3: We can now count the number of faces on each cube, which is 6. Two cubes each having 6 faces equals 12 faces in total. Step 4: The correct answer is – c) 12. a) 2 Refer to Explanation of Answer b) 6 Refer to Explanation of Answer c) 12 Correct Answer d) 14 Refer to Explanation of Answer None Question 95. Taxi company A charges $1.40 per kilometre while Taxi company B charges $1.55 per kilometre. How much do you save by using Taxi company A, if you travel 20 kilometres? Explanation of answer: Step 1: Taxi company A: $1.40 x 10 km would be = $14. Multiply by 2 to get 20 km and $28 for the taxi fare. Step 2: Taxi company A: $1.55 x 10 km would be = $15.50. Multiply by 2 to get 20 km and $31 for the taxi fare. Step 3: $31 subtract $28 = $3. You save $3 by using Taxi company A. Step 4: The correct answer is – b) $3 a) $1.50 Refer to Explanation of Answer b) $3 Correct Answer c) $4.50 Refer to Explanation of Answer d) $5 Refer to Explanation of Answer None Question 96. How many kilowatt hours has this household used? Explanation of answer: Step 1: Reading a power meter, you need to read the dials from left to right. Also you need to read the digits like time on a clock. The hands on the 1000 and 10 dials indicate the number they have past when moving clockwise. The hands on the 10000, 100, and 1 dials indicate the number they have past when moving anticlockwise.. Step 2: The first dial reads 2 as it is just fractionally past the number 2. The second dial reads 0 as the hand is not quite at the 1. The third dial is just past the 7 so it reads 7. The fourth dial is between the 1 and 2, so it is a 1. The last dial has the hand at the 5 so the last digit is a 5. Step 3: The total number of kWh from all 5 dials is: 20,715 kWh. This household has used 20,715 kWh. Step 4: The correct answer is – b) 20,715 kWh. a) 21,825 kWh Refer to Explanation of Answer b) 20,715 kWh Correct Answer c) 21,724 kWh Refer to Explanation of Answer d) 20,814 kWh Refer to Explanation of Answer None Question 97. Matthew got to work at ten minutes to 8am and left at a quarter past 5pm. How long was he at work? Explanation of answer: Step 1: To find out how long Matthew was at work we should break up times into smaller segments and then add them together to find out the total time working. Step 2: 7:50am to 8:00am is 10 mins difference. 8:00am to 12 noon is 4 hours difference. 12 noon to 5pm is 5 hours difference and 5pm to 5:15pm is 15 mins difference. Step 3: Let’s add all this time together. 4 hrs + 5 hrs = 9 hours. 10 mins + 15 mins = 25 mins. 9 hours + 25 mins = 9 hours and 25 mins at work. Step 4: The correct answer is – b) 9 hours and 25 mins. a) 8 hours and 45 minutes. Refer to Explanation of Answer b) 9 hours and 25 minutes. Correct Answer c) 9 hours and 45 minutes. Refer to Explanation of Answer d) 10 hours and 15 minutes. Refer to Explanation of Answer None Question 98. David is on a construction job. He charges $60 per half hour or part thereof. On Wednesday he was on the job for 5 ½ hours, on Thursday he returned for 3 ½ hours, and he finished the job on Friday with 50 minutes of work. How much did he charge for the job? Explanation of answer: Step 1: First piece of information we must note is that David charges $60 per half hour or part thereof. This means he charges $120 per hour. Step 2: Next we need to add up all the time he spent on the job. 5 ½ hours + 3 ½ hours + 50 mins (which we should round up to an hour, as that is what David would charge for) = 10 hours. Step 3: We can either multiply $120 by 10 hours or $60 by 20 half hours. Either way the result is the same. $120 x 10 = $1,200. David charges $1200 for the job. Step 4: The correct answer is – d) $1,200 a) $780 Refer to Explanation of Answer b) $920 Refer to Explanation of Answer c) $1,060 Refer to Explanation of Answer d) $1,200 Correct Answer None Question 99. In the swim leg of the Geelong Ironman, what direction are competitors heading in when they turn around the first turning buoy in the water? Explanation of answer: Step 1: To answer this question you must find the compass on the map. It is located in the top left hand corner of the map. Look for the direction of North and determine the other directions. Step 2: When the swimmers turn around the first turning buoy they are travelling in a South Easterly direction. Step 3: The correct answer is – d) South East a) South West Refer to Explanation of Answer b) North East Refer to Explanation of Answer c) South Refer to Explanation of Answer d) South East Correct Answer None Question 100. 1 gram of protein contains 4 Calories. 1 gram of fat contains 9 Calories. 1 Calorie is equivalent to approximately 4.2 kilojoules. A lamb loin chop contains 11 grams of fat. How many kilojoules of fat are there in the lamb chop? Explanation of answer: Step 1: If we have 11 grams of fat in the lamb chop we should multiply those 11 grams by 9 to figure out how many Calories there are in that chop. 11 x 9 = 99 Calories. Step 2: Next is to figure out the kilojoules. Let’s start by rounding up the 99 Calories to 100. Then we multiply the 100 Calories by 4.2 kilojoules = 420 kilojoules. We have added 1 extra Calorie to round 99 up to 100, so we need to take away the equivalent of 1 Calorie in kilojoules. 1 Calorie = 4.2 kilojoules. We should subtract 4.2 kilojoules from 420 to give us an accurate answer. 420 – 4.2 = 415.8 kilojoules. Step 3: There is 415.8 kilojoules of fat in this lamb loin chop. Step 4: The correct answer is – b) 415.8 kilojoules. a) 412.6 kilojoules Refer to Explanation of Answer b) 415.8 kilojoules Correct Answer c) 416.2 kilojoules Refer to Explanation of Answer d) 418.4 kilojoules Refer to Explanation of Answer None Question 101. 1 gram of protein contains 4 Calories (Cal). 1 gram of fat contains 9 Calories (Cal). 1 Calorie is equivalent to approximately 4.2 kilojoules (kJ). That lamb loin chop contains 672 kilojoules of protein. How many grams of protein are there in the lamb chop? Explanation of answer: Step 1: To find out how many grams of protein we will have to go through several steps. First we will have to convert the kilojoules to Calories, then convert the Calories to grams of protein. Step 2: If we have 672 kilojoules in the lamb chop we will need to divide that 672 by 4.2. This could be quite difficult from 672, however if we break it down we can figure it out. Step 3: We know that 1 Calorie = 4.2 kilojoules and 10 Calories = 42 kilojoules. So 100 Calories = 420 kilojoules. That also means that 50 Calories = 210 kilojoules, which is half of 420. If we add 420 (100 Cal) and 210 (50 Cal) together we get = 630 kilojoules (150 Cal). Our total is 672, so if we subtract 630 from 672 we get 42 kilojoules. This difference is exactly 10 Calories. This means that if we add 420 kJ (100 Cal) + 210 kJ (50 Cal) + 42kJ (10 Cal) = 672 kJ (160 Cal). Step 4: The first line in the question states that there is 4 Calories per 1 gram of protein. Now that we know there are 160 Calories in the lamb chop we can divide that by 4. So 160 ÷ 4 = 40. This means there is 40 grams of protein in the lamb loin chop. Step 5: The correct answer is – b) 40 grams. a) 35 grams Refer to Explanation of Answer b) 40 grams Correct Answer c) 44 grams Refer to Explanation of Answer d) 52 grams Refer to Explanation of Answer None Question 102. Charlie had 5 tests this week. His results are in the table below. What percentage did Charlie score in his S + E test? Explanation of answer: Step 1: If Charlie’s total mark was out of 25 then 25 is ¼ of 100. This means that if we multiply 25 by 4 we would get 100. A score of 100 would give 100%. Step 2: If Charlie got 16 out of 25, then we can multiply 16 by 4 to get his percentage score. 16 x 4 = 64. Alternatively we can do this: 16 x 2 = 32, 32 x 2 = 64. Step 3: Charlie scored 64% in his S + E test. Step 4: The correct answer is – b) 64%. a) 36% Refer to Explanation of Answer b) 64% Correct Answer c) 68% Refer to Explanation of Answer d) 71% Refer to Explanation of Answer None Question 103. Charlie had 5 tests this week. His results are in the table below. Which subject did he perform the best in? Explanation of answer: Step 1: We know that a score of 100 would give 100%, so we need to find out how to get the total marks to 100 and then do the same to his scores. We use multiplication as the tool to find out these percentage scores. Step 2: For English: 20 is 1⁄5 of 100 so we multiply both scores by 5. If he got 14 out of 20, then we can multiply 14 by 5 to get his percentage score. 14 x 5 = 70. Alternatively we can do this: 10 x 5 = 50 + 4 x 5 = 20, 50 + 20 = 70%. English = 70% Step 3: For Math: if the total score is out of 100 then his scores of 73 can already be considered as his percentage score. Math = 73% Step 4: For Science: 50 is ½ of 100 so we multiply both scores by 2. If he got 36 out of 50, then we can multiply 36 by 2 to get his percentage score. 36 x 2 = 72. Alternatively we can do this: 30 x 2 = 60, + 6 x 2 = 12, 60 + 12 = 72%. Science = 72% Step 5: For S + E: 25 is ¼ of 100 so we can multiply both scores by 4. If he got 16 out of 25, then we can multiply 16 by 4 to get his percentage score. 16 x 4 = 64. Alternatively we can do this: 16 x 2 = 32, 32 x 2 = 64%. S + E = 64% Step 6: For Information Technology (I.T.): 20 is 1⁄5 of 100 so we multiply both scores by 5. If he got 15 out of 20, then we can multiply 15 by 5 to get his percentage score. 15 x 5 = 75%. Alternatively we can do this: 10 x 5 = 50, + 5 x 5 = 25, 50 + 25 = 75%. I.T. = 75% Step 7: The correct answer is – e) Information Technology. a) English Refer to Explanation of Answer b) Math Refer to Explanation of Answer c) Science Refer to Explanation of Answer d) S + E Refer to Explanation of Answer e) Information Technology Correct Answer None Question 104. Which of the following shapes could be used to tile a floor without requiring cuts or having any gaps (except for tiles bordering onto the wall)? Explanation of answer: Step 1: To observe each tile in a floor format, look at the pictures below to see if they fit the criteria of the question above. Step 6: The answers are – a, b and c) a) Correct Answer b) Correct Answer c) Correct Answer d) Refer to Explanation of Answer Question 105. Sam spent $16 on spaghetti at the supermarket. Which of the following statements are true? Sam could have bought: Explanation of answer: Step 1: To figure out which statements are correct we need to go through each answer to determine if Sam spent $16 on the spaghetti. Step 2: Two 4 packs (2 x 4 = 8), two 3 packs (2 x 3 = 6) and two single cans (2 x 1 = 2) = 8 + 6 + 2 = $16. Answer is correct. Step 3: Three 4 packs (3 x 4 = 12) and one 3 pack (1 x 3 = 3) = 12 + 3 = $15. Answer is incorrect. Step 4: Four 3 packs (4 x 3 = 12) and four single cans (4 x 1 + 4) = 12 + 4 = $16. Answer is correct. Step 5: Five single cans (5 x 1 = 5), one 3 pack (1 x 3 = 3) and three 4 packs (3 x 4 = 12) = 5 + 3 + 12 = $20. Answer is incorrect. Step 6: The correct answers are – a) Two 4 packs, two 3 packs and two single cans and c) Four 3 packs and 4 single cans. a) Two 4 packs, two 3 packs and two single cans Correct Answer b) Three 4 packs and one 3 pack Refer to Explanation of Answer c) Four 3 packs and 4 single cans Correct Answer d) Five single cans, one 3 pack and three 4 packs Refer to Explanation of Answer Question 106. A car is travelling at 1.5km/min on a Freeway. How fast is the car travelling in kilometres per hour? Explanation of answer: Step 1: If a car was travelling at 1 km per minute on a freeway and there are 60 minutes in an hour, then the car would be travelling at 60km/h. Step 2: As the car is travelling at 1.5 km/min, and we know that 1 km/min = 60 km/h, we can find out what half of 60 is to find the 0.5 km/min. So half of 60 x 0.5 = 30 km/h. Step 3: When we add the 60 km/h and the 30 km/h we get = 90 km/h. The car is travelling at 90km/h. Step 4: The correct answer is – c) 90 km/h Alternative explanation: Step 1: If a car travels 1.5km in 1 minute then it must travel 60 times this distance in 1 hour since there are 60 minutes in an hour. We therefore need to multiply 1.5 by 60. Step 2: To make this easy, break it down. First multiply 1.5 by 10 to get 15. Then multiply 15 by 6 (15 + 15 +15 + 15 + 15 + 15 = 30 + 30 + 30 = 90) to get 90km/h. Step 3: The correct answer is – c) 90km/h a) 80 km/h Refer to Explanation of Answer b) 87 km/h Refer to Explanation of Answer c) 90 km/h Correct Answer d) 102 km/h Refer to Explanation of Answer None Question 107. Peter was looking at the Bureau of Meteorology website to determine how hot it was going to be in January. He lives in Brisbane. What is the chance that Peter will experience a warmer summer than normal? Explanation of answer: Step 1: To determine if Peter will experience a warmer summer than normal we must first look for Brisbane on the map. We can see it is in the dark red area. Step 2: From there we must look at the legend on the right hand side of the image. We must look for the dark red on the legend. When reading the text on the legend we can see that there is a greater than 80% chance of exceeding the median max temperature. This means that there is a very likely chance of the summer being warmer than normal. Step 3: The correct answer is – a) Very likely a) Very likely Correct Answer b) Moderately likely Refer to Explanation of Answer c) Likely Refer to Explanation of Answer d) Not at all likely Refer to Explanation of Answer None Question 108. The graph below shows population from different areas of the world over a one hundred year time period. From 1950 to 2010 the world population appears to have? Explanation of answer: Step 1: The world population in 1950 appears to be about 2.3 billion. In 2010, the world population appears to be about 7 billion. Step 2: This would indicate that the world’s population has tripled from 1950 to 2010 because 2.3 x 3 = 6.9. Step 3: The correct answer is – d) Tripled. a) Doubled Refer to Explanation of Answer b) Halved Refer to Explanation of Answer c) Stayed the same Refer to Explanation of Answer d) Tripled Correct Answer None Question 109. Joseph is looking for a holiday home to rent for 7 nights. He finds one that: Charges $150 per night Has a cleaning fee of $120 Wifi for $8 per night A repayable bond of $300 if there is no damage to the home. What is the total cost of his holiday rental if there is no damage to the home? Explanation of answer: Step 1: Calculate the total cost of the rental fee.7 nights x $150 = $1,050. Step 2: Add the cleaning fee: $1,050 + $120 = $1,170. Step 3: Add wifi (7 nights x $8 = $56): $1,170 + $56 = $1,226. Step 4: He gets the bond back so he does not have to pay the $300. The total cost of the holiday rental is: $1,226. Step 5: The correct answer is – b) $1,226 a) $1,182 Refer to Explanation of Answer b) $1,226 Correct Answer c) $1,410 Refer to Explanation of Answer d) $1,526 Refer to Explanation of Answer None Question 110. Kimberley is building a helicopter model and she is using the scale of 1:50. If the helicopter blades span 18 cms on her model, what is the real life span of the helicopter blades? Explanation of answer: Step 1: The scale in this question means that if you have 1 cm on the model it equals 50 cms in real life. So in this instance, the length of the span on her helicopter blades is 18 cms long. We need to multiply that by 50 to find out the real life span of the helicopter blades. 18 x 50 = ? Step 2: Let’s split the numbers up to make the calculation easier. 10 x 50 = 500 cms. 8 x 50 = 400 cms. 500 cms + 400 cms = 900 cms in length. Step 3: In real life we wouldn’t say that the helicopter blades are 900 cms in length so we must convert to metres. 100 cms = 1 metre. So 900 cms = 9 metres. Step 4: The correct answer is – c) 9.0 m. a) 7.5 m Refer to Explanation of Answer b) 8.8 m Refer to Explanation of Answer c) 9.0 m Correct Answer d) 10.3 m Refer to Explanation of Answer None Question 111. A car was originally priced at $20,000. Its price was reduced by $2,000. There is now a further 5% off the reduced price. How much will the car cost now? Explanation of answer: Step 1: You need to figure out what the reduced cost would be first. So $20,000 minus $2,000 = $18,000. Step 2: From there you need to figure out what 5% of $18,000 is. To do this we start by figuring out 1%. 1% of $18,000 = $180. We can then multiply $180 by 5 and we will get what 5% is worth. So $180 x 5 = $900 ($100 x 5 = $500 + 5 x $80 = $400. $500 + $400 = $900). Alternative step 2: From there you need to figure out what 5% of $18,000 is. To do this we start by figuring out 10% which simply involves dropping one zero off the amount. So 10% of $18,000 is $1,800. To get 5% all we have to do is find half of 10%, so 5% is $1,800 divided by 2 which is $900. Step 3: Then we must subtract $900 from $18,000. $18,000 – $900 = $17,100. The car will now cost $17,100. Step 4: The correct answer is – c) $17,100 a) $18,150 Refer to Explanation of Answer b) $17,800 Refer to Explanation of Answer c) $17,100 Correct Answer d) $16,750 Refer to Explanation of Answer None Question 112. A bar fridge has a width of 500 mm and a depth of 500 mm. If the height is 70 cms, what is the volume of the fridge? Explanation of answer: Step 1: First we must convert the different measurements into the same unit. If the largest measurement is in cms and we need to find volume in cm3 then we can convert the 500 mm to cm. We divide 500 by 10 to get mm into cms. 500 ÷10 = 50 cm. The width and depth is 50 cm each. Step 2: To calculate the capacity of the fridge, we can do this by simply multiplying all three values. 50 cm x 50 cm = 2,500 x 70 = 175,000 cm3. Breakdown: (50 cm x 50 cm = 5 x 5 x 10 x 10 = 25 x 100 = 2,500. Then 2,500 x 70 = 25 x 7 x 100 x 10 = 175 x 1000 = 175,000 cm3. The fridge can hold 175,000 cm3. Step 3: The correct answer is – d) 175,000 cm3 a) 196,000 cm3 Refer to Explanation of Answer b) 187,000 cm3 Refer to Explanation of Answer c) 182,000 cm3 Refer to Explanation of Answer d) 175,000 cm3 Correct Answer None Question 113. Fridges are advertised with their capacity in litres. Use the rule below to figure out how many litres the bar fridge can hold. If the fridge has a capacity of 175,000 cm3, how many litres do this bar fridge hold? Explanation of answer: Step 1: First we must convert the 100 mL to litres. This is done by simply multiplying the 100 mL by 10 =1,000 mL = 1 L. If we do that, we must also convert the 100 cm3 by 10 = 1,000 cm3. This means our rule changes to 1 litre is equivalent to 1,000 cm3. Step 2: To convert from a quantity in cm3 to a quantity in litres, we must divide by 1,000. So 175,000 ÷ 1,000 = 175 (remove all the zeros, as there are three 0’in 1,000 and three 0’s in 175,000). There is 175 L capacity in this bar fridge. Step 3: The correct answer is – c) 175 L. Alternative explanation: Step 1: If 100 ml is equivalent to 100 cm³, then 1,000 ml must be equivalent to 1,000 cm³. 1,000 ml is a litre, so that means that 1 litre is equal to 1,000 cm³. Step 2: If the fridge has a capacity of 175,000 cm³ and 1 litre is 1,000 cm³, then all we have to do is divide 175,000 by 1,000 to get 175 litres. Step 3: The correct answer is – c) 175 L. a) 17.5 L Refer to Explanation of Answer b) 17,500 L Refer to Explanation of Answer c) 175 L Correct Answer d) 1,750 L Refer to Explanation of Answer None Question 114. Matt and Gary were both bowlers in a local cricket team. They were comparing how many runs were scored off their overs. They are: Matt: 3, 3, 4, 5, 8 Gary: 3, 4, 4, 6, 6 Which of the following statements are true? Explanation of answer: Step 1: To know if these statements are correct or not we must understand the mean, mode, median and range of data. These are: Step 2: Mean (average): To find the mean we must add all numbers together then divide by the amount of numbers in the data set. Both data sets add to 23. If we divide by 5 then we would get the same number (23 ÷ 5 = 4.6). Statement c) is correct. Step 3: Median, which is also known as the middle number in the data set. In this case both Matt and Gary have 4 as their middle number. This means that statement d) is correct. Step 4: Mode, which is also known as the most occurring number. Matt’s is 3 and Gary’s is 4, so the mode is different for both players. Statement a) is incorrect Step 5: Range, which is simply the largest number minus the smallest number. Matt’s is: 8 – 3 = 5. Gary’s is 6 – 3 = 3. Matt’s range is higher than Gary’s. Statement b) is correct. Step 6: The correct answer is – b), c) and d). a) Matt and Gary have the same mode Refer to Explanation of Answer b) Matt’s range is higher than Gary’s Correct Answer c) Matt’s and Gary’s mean are the same Correct Answer d) The median is the same for both players Correct Answer Question 115. At the Perth Arena, Keanu sat in the light blue section of block 214. His friend Tim sat in the yellow section of block 204. Which of the following statements are true? Explanation of answer: Step 1: Adjacent means next to so statement a) is incorrect. Step 2: The yellow section in block 204 is next to a stairway and exit, so statement b) is correct. Step 3: The navy blue section is right in front of the court, so statement c) is incorrect. Step 4: Opposite in this case means the other side. So Tim is sitting opposite Keanu. Statement d) is correct. Step 5: The correct answers are – b) and d). a) Keanu sat in the adjacent block to Tim Refer to Explanation of Answer b) Tim is sitting near a stairway and exit Correct Answer c) Keanu sat right in front of the court Refer to Explanation of Answer d) Tim sat in the opposite block to Keanu Correct Answer Question 116. The Star Wars Films were not made in numerical (or episode) order. There was a 21 year difference in release dates between Episode IV: A New Hope and Episode I: The Phantom Menace. How many years have passed between Episode VI: Return of the Jedi and Episode I: The Phantom Menace? Explanation of answer: Step 1: Episode VI: Return of the Jedi was released in 1983, while Episode I: The Phantom Menace was released in 1999. Step 2: We do count the year that a film was released in so we have to count from 1983 to 1999. In this case it was 16 years (1999 – 1983 = 99 – 83 = 16). Step 3: The correct answer is – c) 16 years a) 20 years Refer to Explanation of Answer b) 18 years Refer to Explanation of Answer c) 16 years Correct Answer d) 15 years Refer to Explanation of Answer None Question 117. In a 5 x 5 grid D4 is South East of B2. What direction is B4 from D1? Explanation of answer: Step 1: As there is no compass in this question, you must have a good knowledge of the compass directions and there is a hint in the question. If D4 is South East of B2 then we can figure out that B4 is in the North East of the grid and D1 is in the South West of the grid. This means that the direction from D1 to B4 is in a North East direction. Step 2: B4 to D1 is in the North East direction. Step 3: The correct answer is – a) North East. a) North East Correct Answer b) East Refer to Explanation of Answer c) North West Refer to Explanation of Answer d) South East Refer to Explanation of Answer None Question 118. Which of the following expressions represents the proportion of red smarties in the picture? Explanation of answer: Step 1: There are 2 red smarties out of 20 smarties all together. This can be represented as a fraction as 2⁄20 which when simplified is the same as 1⁄10. This answer is correct. Step 2: 1⁄10 when converted into a decimal is 0.10. This answer is correct. Step 3: 0.10 as a decimal is the same as saying 10%. This answer is correct. Step 4: 1 represents 1 whole or in this case with these smarties is 20⁄20 or 100%. This answer is not correct. Step 5: The correct answers are – a), c), and d) a) 10% Correct Answer b) 1 Refer to Explanation of Answer c) 1⁄10 Correct Answer d) 0.10 Correct Answer Question 119. During the summer time in Australia, NSW switches to Daylight Savings Time. This means that Sydney would be 3 hours ahead of Perth. What is the time in Perth, if it is 15:45 in Sydney? Explanation of answer: Step 1: As this question is in 24 hour time we must work in 24 hour time. If you need to know what the time is in 12 hour time, subtract 12:00 from 15:45 and you get 3:45pm. Step 2: If the time in Sydney is 15:45 and Sydney is 3 hours in front of Perth, then we have to subtract 3 hours from 15:45 to find out Perth time. So 15:45 – 03:00 hours = 12:45 Step 3: Perth time would be 12:45 Step 4: The correct answer is – d) 12:45 a) 11:45 Refer to Explanation of Answer b) 18:45 Refer to Explanation of Answer c) 17:45 Refer to Explanation of Answer d) 12:45 Correct Answer None Question 120. Layla cooks a lamb roast in the oven for 2 1⁄2 hours and then leaves it in the oven for another 1⁄4 of an hour to cool slightly. What is the total number of hours that the lamb roast was in the oven? Explanation of answer: Step 1: First we add the fractions together. 2 1⁄2 hours + 1⁄4 hour = 2 3⁄4 hours. Step 2: We know that the 2 means 2 hours but we need to figure out what 3⁄4 is as a decimal. If 0.5 = 1⁄2 as a fraction and 0.25 = 1⁄4 as a fraction, then 3⁄4 would equal 0.75. So 3 quarters of an hour (or 45 mins) would be represented as 0.75 as a decimal. Step 3: So this means that the Lamb roast was in the oven for 2.75 hours. Step 4: The correct answer is – c) 2.75 hours. a) 2.5 hours Refer to Explanation of Answer b) 3 hours Refer to Explanation of Answer c) 2.75 hours Correct Answer d) 3.25 hours Refer to Explanation of Answer None Question 121. If four 1 kg bags of mixed cereal grains cost $96, how much would seven and a half 1 kg bags cost? Explanation of answer: Step 1: We need to figure out what one 1 kg bag costs. We have to divide 96 by 4 to find our answer. We could round up the $96 to $100 and divide by 4, which would give us $25 or 4 lots of $25. As we have rounded up by 4, we should subtract $1 from each group of $25. This means that the 1 kg bag would cost $24. Alternatively we can split up the $96 into $80 and $16 and divide each by 4 (80 ÷ 4 = 20, 16 ÷ 4 = 4). This gives us 20 + 4 = $24. Step 2: Now that we know that each 1 kg bag is $24 we have to multiply that 7.5. It would be easier to split these numbers again to 7 and 0.5. 7 x 24 (7 x 20 = 140 and 7 x 4 = 28, so 7 x 24 = 140 + 28 = 168). 0.5 x 24 (½ x 24) = 12. 168 + 12 = 180. The 7.5 1 kg bags of mixed cereal would cost $180. Step 3: The correct answer is – d) $180 a) $164 Refer to Explanation of Answer b) $168 Refer to Explanation of Answer c) $175 Refer to Explanation of Answer d) $180 Correct Answer None Question 122. Harry was going to a National Basketball League game. He had to travel on the train to and from the game plus purchase tickets for the game. The game tickets cost $64. The return train ride cost $15. How much did his trip out to watch the game cost him? Explanation of answer: Step 1: Simply add the two values together. $64 plus $15 = $79. Note that a “return” trip is a two-way trip, so we don’t double the $15 train fee to cover each leg of the journey. Step 2: The correct answer is – b) $79. a) $83 Refer to Explanation of Answer b) $79 Correct Answer c) $75 Refer to Explanation of Answer d) $68 Refer to Explanation of Answer None Question 123. Sandy went to the Sydney Opera House to watch a performance. She was sitting in the Box B area. She was sitting in seat 34. Explanation of answer: Step 1: She is not sitting directly in front of the platform, so statement a) is incorrect. Step 2: Box D is not directly next to (adjacent) Box B, so statement b) is incorrect. Step 3: She is not near Door 14, she is near Door 5 or Door 6, so statement c) is incorrect. Step 4: When reading the seat numbers in Box B, there are 68 seats available. Seat 34 is the middle number between 1 and 68. So she is sitting right in the middle of Box B. Statement c) is correct. Step 5: The correct answers is – c) She is sitting right in the middle of the Box B area. a) Sandy is sitting directly in front of the platform Refer to Explanation of Answer b) Box D is directly adjacent to where Sandy is sitting Refer to Explanation of Answer c) She is sitting right in the middle of the Box B area Refer to Explanation of Answer d) She is near Door 14 Refer to Explanation of Answer None Question 124. Mandy used this ice tray to make ice cubes for her water cooler. Explanation of answer: Step 1: Look at the ice tray and count the amount of holes. Step 2: The answer is 8 holes. Step 3: The questions says Mandy filled it 7 times. Step 4: This means you need to multiply 8 times 7 to get the total number of ice cubes. Step 5: The correct answer is – a) 56 ice cubes. a) 56 Correct Answer b) 52 Refer to Explanation of Answer c) 48 Refer to Explanation of Answer d) 44 Refer to Explanation of Answer None Question 125. Dana is a baker. She is making hot cross buns at her store for Easter. She packages them into boxes of 6. She made 220 hot cross buns. How many hot cross buns were left over? Explanation of answer: Step 1: To find out how many hot cross buns were left over we need to divide 220 by 6. To find an easier way to do this lets bunch the boxes of 6 into groups of 10. This means that there are 60 hot cross buns per bundle of ten packets. We know that in one bundle there are 60 hot cross buns, in two bundles 120, in three bundles 180, in 4 bundles 240 hot cross buns. Since we only have 220, we don’t have 4 bundles of 10. It must be 3 bundles (180 hot cross buns) plus some extra packets. Step 2: So we have 3 bundles of hot cross buns giving us 180 hot cross buns. We can now use the 6 times tables to figure out how many packets there are left. If we multiply 6 x 6 we get 36 hot cross buns. If we add 180 plus 36 we get 216 hot cross buns. We are 4 short of 220 hot cross buns. Step 3: This means that there are 36 packets of 6 hot cross buns, with 4 hot cross buns left over. Step 4: The correct answer is – c) 4 a) 8 Refer to Explanation of Answer b) 6 Refer to Explanation of Answer c) 4 Correct Answer d) 3 Refer to Explanation of Answer None Question 126. The Hawaii Ironman event is considered one of the most gruelling and challenging Ironman events in the world. The record for the fastest time completing the event was set in 2011 at 8 hours 3 minutes and 56 seconds. If the world record for finishing the race is at 3:03:56 pm, what is starting time of the race? Explanation of answer: Step 1: If the race finished at 3:03:56 pm and we know that it took 8 hours, 3 minutes and 56 seconds to complete then we need to subtract that total from the finishing time. Step 2: 3 pm minus 8 hours = 7 am (3 hours to noon, then 5 hours to 7 am). Our time now is 07:03:56. We then can subtract 3 minutes and 56 seconds from the total to give us 7:00 am (07:03:56 – 00:03:56 = 07:00:00). Step 3: The correct answer is – a) 7:00 am a) 7:00 am Correct Answer b) 7:13 am Refer to Explanation of Answer c) 7:15 am Refer to Explanation of Answer d) 7:30 am Refer to Explanation of Answer None Question 127. A small cafe in the city decided to keep a tally of the amount of coffees customers bought each week. How many customers purchased more than 6 coffees in the week. Explanation of answer: Step 1: The question asks how many customers purchased more than 6 coffees in a week. This means that we need to count the three numbers in the three rows that tell us how many customers bought 7 to 15 coffees in the week. Step 2: We need add 8 + 5 + 2 to get the amount of customers buying more than 6 coffees. This equals 15 customers that bought more than 6 coffees in the week. Step 3: The correct answer is – c) 15. a) 10 Refer to Explanation of Answer b) 12 Refer to Explanation of Answer c) 15 Correct Answer d) 18 Refer to Explanation of Answer None Question 128. A plumber turns a tap handle through 5 full revolutions to turn it off. How many degrees did he turn the tap handle through? Explanation of answer: Step 1: The question states that the bulb was rotated through 5 full revolutions. One revolution is 360 degrees so we need to multiply 360 by 5 to get our answer. Step 2: Let’s break down the number 360 into two parts; 300 and 60. Let’s multiply 300 by 5 = 1500. Let’s multiply 60 by 5 = 300. Add 1,500 and 300 together to give = 1,800. Step 3: The plumber had to turn the tap handle through 1,800 degrees to turn the tap off. Step 4: The correct answer is – a) 1,800 degrees. a) 1,800 degrees Correct Answer b) 1,650 degrees Refer to Explanation of Answer c) 1,500 degrees Refer to Explanation of Answer d) 1,350 degrees Refer to Explanation of Answer None Question 129. Anna bought 11 packets of 6 bread rolls for $3.20 each. She paid with a $50 note. How much change should she receive? Explanation of answer: Step 1: To find this answer we should multiply $3.20 by 11. However, if we multiply $3.20 by 10 and then add $3.20 to the total we will get the same answer. 10 x $3.20 = $32.00 + $3.20 = $35.20. Step 2: We now need to find the change from a $50 note. $50 – $35.20 ($50 – $35 = $15, and $15.00 – $0.20 = $14.80) = $14.80. Step 3: Anna received $14.80 change from the $50 note. Step 4: The correct answer is – b) $14.80 a) $13.40 Refer to Explanation of Answer b) $14.80 Correct Answer c) $15.20 Refer to Explanation of Answer d) $16.30 Refer to Explanation of Answer None Question 130. John was building a play house for his children. He measured the top section for some beams that he needed for the roof. As he was building one of the other sections he realised that the original measurement for the roof was incorrect. He needed an additional 15% of wood for the beam. The original measurement for the beam was 1,800 mm. What does the new length of the beam need to be? Explanation of answer: Step 1: We know that the original beam was 1,800 mm and that we need an additional 15% of that beam to make part of the roof. So we need to find 15% of 1,800 and then add it to 1,800. Step 2: 10% of 1,800 would be 180. To find 10% we can remove one 0 from 1,800 to get the total of 180. As 5% is half of 10% we can halve the 180 to find 5%. 180 ÷ 2 = 90. Now to get 15% we add the 180 (10%) and 90 (5%) together to give 270. Step 3: We now have the extra 15% which equals 270 mm. Now add 270 mm to 1,800 mm to give the new length of beam required. 1,800 mm + 270 mm = 2,070 mm. Step 4: The correct answer is – b) 2,070 mm. a) 2,050 mm Refer to Explanation of Answer b) 2,070 mm Correct Answer c) 2,095 mm Refer to Explanation of Answer d) 2,115 mm Refer to Explanation of Answer None Question 131. The tables below show the fare for a Transperth ride for adults and children (concession). A Family Rider fare can be purchased for up to seven people What would be the cheapest price for 2 adults and 3 children to travel 2 zones paying cash? Explanation of answer: Step 1: When attempting to answer this question, make sure your read the table and following information correctly. There is one row in the standard fare table that has a FamilyRider fare and after the table is a statement that determines how many people can travel on a FamilyRider fare. This option is available to purchase for a group of up to seven people to ride on Transperth services all day regardless of zones travelled. Step 2: A FamilyRider would cost $12.40. While 2 adults travelling two zones is 2 x $4.60 = $9.20 and 3 children travelling two zones is 3 x $1.90 = $5.70. $9.20 + $5.70 = $14.90. The FamilyRider would be the cheapest price to travel the 2 zones at $12.40. Step 3: The correct answer is – c) $12.40 a) $14.90 Refer to Explanation of Answer b) $13.75 Refer to Explanation of Answer c) $12.40 Correct Answer d) $11.85 Refer to Explanation of Answer None Question 132. A survey was taken on 150 people about what is their favourite sport to watch on television. The table below shows the results of that survey. Out of the 150 people surveyed, how many females watch AFL and BBL cricket as their favourite sports to watch? Explanation of answer: Step 1: The way to answer this question is to first look at the female row. Scan across until you see the values for AFL (37) and BBL Cricket (14). These two numbers need to be added together to give us the answer. Step 2: 37 + 14 = 51. There are 51 females whose favourite sports to watch are AFL and BBL Cricket. Step 3: The correct answer is – b) 51 a) 47 Refer to Explanation of Answer b) 51 Correct Answer c) 56 Refer to Explanation of Answer d) 62 Refer to Explanation of Answer None Question 133. Corey had a pool table measuring 1.4 m by 2.4 m. He wanted to place a large rectangular piece of carpet under the table so that people were comfortable when playing pool. He decided that he needed an additional 70 cm all around the pool table. What is the minimum size of carpet he needs to fit around the pool table? Explanation of answer: Step 1: Imagine a pool table as a rectangle. The carpet that will fit under the pool table is a larger rectangle around the smaller rectangle. This means that Corey should add 70 cm of carpet on every side of the pool table. Step 2: For the width, we should add 1.4 m + 0.7 m (70 cm) + 0.7 (70 cm) = 2.8 m Step 3: For the length, we should add 2.4 m + 0.7 m (70 cm) + 0.7 (70 cm) = 3.8 m Step 4: This means the dimensions for the carpet are: 2.8 m by 3.8 m Step 5: The correct answer is – d) 2.8 m by 3.8 m. a) 1.8 m by 2.6 m Refer to Explanation of Answer b) 2.2 m by 2.8 m Refer to Explanation of Answer c) 2.5 m by 3.4 m Refer to Explanation of Answer d) 2.8 m by 3.8 m Correct Answer None Question 134. Scott was visiting Perth and wanted to see several sites in the city. He decided to catch the Perth CAT bus service. His hotel was on the corner of Hay St and Plain St. What colour and number bus stop is closest to his hotel? Explanation of answer: Step 1: There are two ways you can find the answer to this question. You can either look for each answer (colour and numbered bus stop) on the map or look for the two streets and then the corresponding bus stop. Step 2: In this case we will look for Hay St which runs left to right through the centre of Perth. Plain St is located on the far right of the map running top to bottom. Once you have found the intersection look for the closest bus stop. This bus stop is Red 29. Step 3: The closest bus stop to Scott’s hotel is Red 29. Step 4: The correct answers is – c) Red 29. a) Blue 14 Refer to Explanation of Answer b) Yellow 30 Refer to Explanation of Answer c) Red 29 Correct Answer d) Green 20 Refer to Explanation of Answer None Question 135. At the beginning of 2017 the population of New Zealand was 4,747,443. What is New Zealand’s population to the nearest thousand? Explanation of answer: Step 1: The question asks to round the New Zealand population to the nearest thousand. Step 2: You need to round 4,747,443 to the nearest thousand. Step 3: Look at the number in the thousands column, it is 7. Step 4: When rounding we need to look at the number on the right hand side of the number being rounded. In this case it is 4. Step 5: Because the 4 is closer to 0 than it is to 10, we must keep the 7 in the same the thousands column followed by three 0’s. This gives us 4,747,000. Step 6: The correct answer is – a) 4,747,000. a) 4,747,000 Correct Answer b) 4,757,000 Refer to Explanation of Answer c) 4,746,000 Refer to Explanation of Answer d) 4,748,000 Refer to Explanation of Answer None Question 136. A cylinder is cut in half from top to bottom to form two half cylinders. How many straight edges are there on both half cylinders combined? Explanation of answer: Step 1: The best way to explain how many sides there are on both half cylinders is to show a diagram of a half cylinder. Step 2: Step 3: When observing the half cylinder we can see that there are 4 straight lines. As the question asks for all the straight edges on both half cylinders then we should multiply the 4 by 2 to gives us 8 straight edges. Step 4: The correct answer is – c) 8. a) 4 Refer to Explanation of Answer b) 6 Refer to Explanation of Answer c) 8 Correct Answer d) 10 Refer to Explanation of Answer None Question 137. Chris was laying reticulation pipe to water his garden. The length of each pipe was 2,400 mm. He had to buy 12 pipes for his system. What was the total length of all the pipes he had to buy in metres? Explanation of answer: Explanation of answer: Step 1: We can answer this question in two ways. We can either convert each pipe from millimetres to metres or we can find out the total in millimetres then convert to metres. Let’s convert each pipe into metres then find out the total Step 2: There are 1,000 millimetres in 1 metre, so we can divide 2,400mm by 1,000 to give us a total in metres. 2,400 ÷ 1,000 = 2.4. Each pipe is 2.4 metres long. Step 3: Chris had to buy 12 pipes so we need to multiply 12 by 2.4. Let’s break down the 12 in to a 10 and 2 then multiply by 2.4. We then add the two totals together. 10 x 2.4 = 24 and 2 x 2.4 = 4.8, then 24 + 4.8 = 28.8. Chris had to buy 28.8 metres of reticulation pipe. Step 3: The correct answer is – b) 28.8 m a) 26.4 m Refer to Explanation of Answer b) 28.8 m Correct Answer c) 30.2 m Refer to Explanation of Answer d) 31.6 m Refer to Explanation of Answer None Question 138. In the Smith family budget, they allocate $4,500 a month for bills and mortgage. The ratio of spending for food to bills and mortgage is 1:3.5. How much do they spend on food? Explanation of answer: Step 1: The scale in this question means that if you have $1 spent on food you spend $3.50 on bills and mortgage. This is a part to part ratio, which means that the $4,500 needs to split into 4.5 parts. $4,500 divided by 4.5 = $1,000, which means 1 part = $1000. This means the Smith family spends $1000 on food. Step 2: The correct answer is – b) $1,000. a) $1,100 Refer to Explanation of Answer b) $1,000 Correct Answer c) $900 Refer to Explanation of Answer d) $750 Refer to Explanation of Answer None Question 139. What are the correct expressions to show how much pizza Stan has? Explanation of answer: Step 1: The picture shows us that we have 2 full pizzas and one pizza with 3 pieces left. This can be represented in different forms. They are: Step 2: As a fraction: 23⁄5. 2 full pizzas and 3 out of 5 pieces left. Step 3: 23⁄5 is the same as saying 260% because 2 + 3⁄5 = 2 + 6⁄10 = 2 + 60⁄100 = 200 + 60⁄100 = 260⁄100 Step 4: 260% is the same as saying 2.6 in decimals. Step 5: 14⁄5 isn’t correct as we do not have 14 pieces of pizza remaining (which is represented by the numerator). Step 4: The correct answers are- a) 2.6, b) 260%, c) 23⁄5 a) 2.6 Correct Answer b) 260% Correct Answer c) 23⁄5 Correct Answer d)14⁄5 Refer to Explanation of Answer Question 140. Robert was preparing a grassed area for his children to play on. The width was 6 m and the length was 9 m. After preparing the area he needed to buy roll on grass which cost $10 a square metre. How much did it cost Robert for the roll on grass? Explanation of answer: Step 1: First we need to find the area for the grass. 6 m x 9 m = 54 m2. Step 2: The question states that is costs $10 per square metre of roll on grass. 54 m2 x $10 = $540. Step 3: Cost of roll on grass was $540. Step 4: The correct answer is – c) $540. a) $380 Refer to Explanation of Answer b) $470 Refer to Explanation of Answer c) $540 Correct Answer d) $620 Refer to Explanation of Answer None Question 141. Bianca’s recipe for 10 banana muffins is 400g flour 500g sugar 2 eggs 300g of banana 20g baking soda a) If Bianca wants to make 16 muffins, how much sugar does she need to use? Please select your answer a) 640g Refer to Explanation of Answer b) 700g Refer to Explanation of Answer c) 780g Refer to Explanation of Answer d) 800g Correct Answer b) If Bianca gives away half of her muffins and eats 1 muffin, how many muffins does she have now? Please select your answer a) 3 Refer to Explanation of Answer b) 5 Refer to Explanation of Answer c) 7 Correct Answer d) 9 Refer to Explanation of Answer Explanation of answer: Step 1: Firstly we know that 10 muffins needs 500g of sugar in the recipe. We need to find out how much sugar is needed for 6 muffins. Step 2: To do this we need to find out how much sugar is needed for 1 muffin. To find this we divide 500g by 10 = 50g. One muffin takes 50g of sugar to make. If we now multiply 50g by 6 we will get the amount of sugar we need. 50g x 6 = 300g. To make the extra 6 muffins Bianca needs an additional 300g of sugar. Step 3: We now need to add the 500g and 300g to find out the total amount of sugar needed for the 16 muffins. 500g + 300g = 800g. Step 4: This is the correct answer for a) 800g Step 5: Bianca gives away half of her muffins. This means we need to divide the total by 2. 16 ÷ 2 = 8. Bianca then eats one herself. This means we subtract 1 muffin from the total. 8 – 1 = 7. She has 7 muffins left. Step 6: This is the correct answer for b) 7 Question 142. Georgie wanted to buy some new shoes. The shoes cost $60 a pair. When she went to pay for the shoes, the sales assistant said there was special deal for buying shoes. She could buy one pair of shoes and get ¼ off the price of the second pair of shoes. How much did Georgie pay for the two pairs of shoes? Explanation of answer: Step 1: The first step in answering this question would be to find the ¼ off the $60. ¼ is a ½ of a ½. Half of $60 is $30 and half of $30 is $15. $15 is a ¼ of $60. Now we need to subtract $15 from $60. $60 – $15 = $45. Step 2: We now have our two prices for the shoes. The first pair is $60 and the second pair is $45. We need to add these two values together to find our total cost. So $60 + $45 = $105. Step 3: The cost of the two pairs of shoes is $105. Step 4: The correct answer is – a) $105 a) $105 Correct Answer b) $95 Refer to Explanation of Answer c) $60 Refer to Explanation of Answer d) $35 Refer to Explanation of Answer e) $15 Refer to Explanation of Answer None Question 143. A swimmer is training for an international event. The swimmer swims 3.4 kilometres 3 times a week and also swims on the weekend. The total distance for the week is 21 kilometres. What is the distance swum on the weekend? Explanation of answer: Step 1: To find out the total distance swum on the weekend we must first find out how many kilometres they have swum during the week. That person swum 3.4 km, 3 times a week. So 3 x 3 km = 9 km and 3 x 0.4 km = 1.2 km. 9 km + 1.2 km = 10.2 km. Step 2: Now that we know they swum 10.2 km during the week we can subtract that total from 21 km to give us the distance swum on the weekend. 21 km – 10.2 km = 10.8 km. Step 3: Alternatively we can do it this way: 21 km – 10 km = 11 km. 11 km – 0.8 km = 10.8 km. Step 4: They swum 10.8 km on the weekend. Step 5: The correct answer is – d) 10.8 km a) 5.6 km Refer to Explanation of Answer b) 7.3 km Refer to Explanation of Answer c) 9.2 km Refer to Explanation of Answer d) 10.8 km Correct Answer None Question 144. A triangular pyramid has three edges on its base and three edges reaching to the apex of the pyramid. This gives a total of 6 edges for a triangular pyramid. A square pyramid has four edges on its base and four edges reaching to the apex of the pyramid. This give a total of 8 edges for a square pyramid. How many edges would a hexagonal pyramid have? Explanation of answer: Step 1: First we must know how many edges a hexagon has to determine how many edges in a hexagonal pyramid. Hex means six, so a hexagon has six sides and a hexagonal pyramid’s base would have six edges. Step 2: If we look at the pattern developed in the other pyramids, 3 edges on the base, 3 edges to the apex = 6 edges. 4 edges on the base, 4 edges to the apex = 8 edges. We can deduce that 6 edges on the base and 6 edges to the apex will give 12 edges on this type of pyramid. Look at this model to check: Step 3: The amount of edges on a hexagonal pyramid would be 12. Step 4: The correct answer is – c) 12 edges a) 5 edges Refer to Explanation of Answer b) 9 edges Refer to Explanation of Answer c) 12 edges Correct Answer d) 14 edges Refer to Explanation of Answer None Question 145. Logan went to the rugby with $70. He bought three items and had $22 in his pocket at the end of the game. Select the three items that Logan bought. Explanation of answer: Step 1: The question says that $70 was used and there was $22 left in his pocket, this means that $48 was spent. You need to find out what three items added together came to $48. Step 2: To make $48, we will need to make sure the hat is included as it represents the largest cost within the total of $48. Notice that adding the cost of items B, C & D together gives $6 + $5 + $8 = $19 which is far less than the $48 dollars that was spent. This is why the hat must be one of the three items purchased. Step 3: Add items A, B & C together. $35 + $6 + $5 = $46. Not the correct answer. Step 4: Add items A, C & D together. $35 + $5 + $8 = $48. The correct answer. Step 5: Add item A, B & D together. $35 + $6 + $8 = $49. Not the correct answer. Step 7: As there are multiple combinations of items to get to the correct answer of $48, this question requires a process of elimination to determine the correct answer. This process is shown above. Step 8: The correct answer is – c) A, C & D. a) A, B & C Refer to Explanation of Answer b) B, C & D Refer to Explanation of Answer c) A, C & D Correct Answer d) A, B & D Refer to Explanation of Answer None Question 146. Thomas was looking at Perth City on google maps. He measured the straight-line distance between the WACA ground and Perth Arena to be approximately 3 centimetres. Thomas looked up the real straight line distance between WACA ground and Perth Arena. It is approximately 3 kilometres. What is the scale ratio of the google map that Thomas was looking at? Explanation of answer: Step 1: The first thing we know is that 3 centimetres on the map is equal to 3 kilometres in real life. We need to convert that 3 kilometres into centimetres to find out our scale ratio. Step 2: 3 kilometres is the same as saying 3,000 metres (1,000 metres in 1 kilometre). 3,000 metres is the same as saying 300,000 centimetres (100 centimetres in 1 metre). Step 3: So therefore 1 centimetre on the map is equal to 100,000 centimetres on the ground. We know this because 300,000 cm ÷ 3 cm = 100,000 cm. Step 4: The correct answer is – d) 1 : 100,000 a) 1 : 100 Refer to Explanation of Answer b) 1 : 1,000 Refer to Explanation of Answer c) 1 : 10,000 Refer to Explanation of Answer d) 1 : 100,000 Correct Answer None Question 147. The internal playing surface of a 7 foot English pool table is 180 cm by 90 cm. When adding on the cushion and frame the pool table is larger in size. If the cushion and frame are an extra 13 cm on each side of the table, what is the total length and width of the pool table in metres? Explanation of answer: Step 1: The cushion and frame of the pool table are 13 cm per side. With the table being a rectangle there are two sides in the length direction and two sides in the width direction. We must therefore add 2 x 13 = 26 cm to each internal dimension to work out what the external dimensions are since the question asks for the “total length and width”. Step 2: We need to add 26 cm to the internal length. 180 cm + 26 cm = 206 cm Step 3: We need to add 26 cm to the internal width. 90 cm + 26 cm = 116 cm Step 4: We need to convert 206 cm and 116 cm into metres. As 1 m = 100 cm we can convert these numbers. Step 5: 206 cm = 2.06 m Step 6: 116 cm = 1.16 m. Step 7: This means the pool table dimensions are 2.06 m by 1.16 m. Step 8: The correct answer is – c) 2.06 m by 1.16 m. a) 1.67 m by 0.77 m Refer to Explanation of Answer b) 1.93 m by 1.03 m Refer to Explanation of Answer c) 2.06 m by 1.16 m Correct Answer d) 2.10 m by 1.20 m Refer to Explanation of Answer None Question 148. Ethan went to the local community fair. Whilst he was there he bought a wooden hand-made toy for $14 and a painting for $27. How much in total did Ethan spend? Explanation of answer: Step 1: Simply add the two values together. $27 + $14 = $41. Step 2: The correct answer is – c) $41. a) $32 Refer to Explanation of Answer b) $36 Refer to Explanation of Answer c) $41 Correct Answer d) $43 Refer to Explanation of Answer None Question 149. Jack went to the Melbourne Town Hall as part of the Melbourne International Comedy Festival. His ticket was in A reserve, section DD, seat 47. His friend Ben was C reserve, section QQ, seat 34. Which statements are true? Explanation of answer: Step 1: Jack’s seat is number 47, the end of the row is seat 52. Jack’s seat is 4 away from the walkway. So he is near a walkway. Statement a) is correct. Step 2: Jack’s seat is on the balcony so his seat is not on the lower floor. Statement b) is incorrect. Step 3: Ben, is sitting in C reserve, section QQ, seat 34. This seat is further away from the stage than Jack’s. So Jack is sitting closer to the stage than Ben. Statement c) is correct. Step 4: Section CC is adjacent to section DD. Section GG is on the other side of the Hall so statement d) is incorrect. Step 5: The correct answers are – a) Jack is near a walkway and c) Jack is sitting closer to the stage than his friend Ben. a) Jack is near a walkway Correct Answer b) His seat is on the lower floor Refer to Explanation of Answer c) Jack is sitting closer to the stage than his friend Ben Correct Answer d) Section GG is directly adjacent to where Jack is sitting Refer to Explanation of Answer Question 150. In the winter months, Australia and New Zealand do not have daylight savings time. There is a 2 hour time difference between Perth and Brisbane and another 2 hour time difference between Brisbane and Wellington. It was 16:35 in Perth and Tegan wanted to call family in Brisbane and Wellington. Tegan spent 30 mins talking to her Uncle in Wellington. She then rang her Dad in Brisbane. What time was it in Brisbane when Tegan rang her Dad? Explanation of answer: Step 1: There is a lot of information in this question, but some of it is not needed to work out the answer. The first part helps you to know the time difference between the 3 cities. The second part will help you determine the answer. Let’s work with the second part of information first. Step 2: If it is 16:35 in Perth and Tegan makes a 30 minute phone call, then the time she hangs up will be 17:05. This is exactly 30 mins after 16:35 and will be the time she makes her second phone call. Step 3: Now that we know the time Tegan will make the second phone call from Perth, we need to add the 2 hours time difference between Perth and Brisbane. 17:05 + 02:00 = 19:05. Step 4: The time Tegan rand her Dad in Brisbane was 19:05. Notice that we never needed to know the time difference between Brisbane and Wellington – this information just makes the question sound more complicated than it really is. Step 5: The correct answer is – d) 19:05 a) 18:05 Refer to Explanation of Answer b) 18:45 Refer to Explanation of Answer c) 19:00 Refer to Explanation of Answer d) 19:05 Correct Answer None Question 151. Bob and his friends regularly volunteer at a soup kitchen. The weekly roster for all the friends is below. How many days were Joe, Mia and Helen rostered to work on the same day? Explanation of answer: Step 1: Let’s find the days that Joe, Mia and Helen each worked and then we can see if they worked on the same days. We are looking for the green rectangles under each name as they are the days they worked. Step 2: Joe worked: Monday, Thursday and Sunday. Step 3: Mia worked: Monday, Thursday and Friday. Step 4: Helen worked: Monday, Saturday and Sunday. Step 5: The only common day they all worked was Monday. They were only rostered to work 1 day together. Step 6: The correct answer is – b) 1 day a) 0 days Refer to Explanation of Answer b) 1 day Correct Answer c) 2 days Refer to Explanation of Answer d) 4 days Refer to Explanation of Answer None Question 152. Gabriel went to the shop to buy some chewing gum. In one packet there were 14 sticks of gum. He bought 3 packets. How many sticks of gum did he have in total? Explanation of answer: Step 1: If there were 14 sticks in one packet and Gabriel bought 3 packets, we have to multiply 14 by 3 to find out how many sticks of gum in total. Step 2: We can break the 14 into two totals, 10 and 4 and multiply them each by 3. 10 x 3 = 30 and 4 x 3 = 12. We then add the two totals together to give us our final answer. 30 + 12 = 42. Step 3: The total amount of sticks of gum is 42. Step 6: The correct answer is – d) 42 a) 32 Refer to Explanation of Answer b) 36 Refer to Explanation of Answer c) 40 Refer to Explanation of Answer d) 42 Correct Answer None Question 153. Isla has 3 bags of Snakes from The Natural Confectionery Company. There are 18 snakes in each bag. She wants to divide up the snakes in 5 bags for herself and her friends. If she divides up the snakes equally per bag, how many snakes are left over? Explanation of answer: Step 1: This question requires you to find out how many snakes Isla has and then divide them into the paper bags equally. We need to multiply 3 bags of 18 snakes: 3 x 18 = 54 snakes (3 x 10 = 30, 8 x 3 = 24, and 30 + 24 = 54). Step 2: As we have 5 bags we want to be working with multiples of 5. 50 and 55 are multiples of 5, but 54 is not. We can divide 50 snakes into the 5 bags equally. 50 ÷ 5 = 10, so each bag would get 10 snakes. This leaves us with 4 snakes left over that cannot be divided equally into the bags. Step 3: Isla is left with 4 snakes that can’t be placed equally into the bags. Step 4: The correct answer is – b) 4. a) 3 Refer to Explanation of Answer b) 4 Correct Answer c) 5 Refer to Explanation of Answer d) 7 Refer to Explanation of Answer None Question 154. Kayla left work early to attend an appointment. It took her 25 minutes to drive to the appointment. The appointment took 30 minutes. She then had to drive home which took her 45 minutes. She arrived home at 6:10pm. What time did Kayla leave work for her appointment? Explanation of answer: Step 1: There are several times that we must consider in trying to figure out when Isla left work. We should add all the times spent travelling and the appointment time first. Step 2: Travel time 1 = 25 mins, appointment time = 30 mins, travel time 2 = 45 mins. 25 mins + 30 mins = 55 mins. 55 mins + 45 mins = 1 hour and 40 mins. Isla spent 1 hour and 40 mins travelling and at the appointment. Step 3: Isla got home at 6:10pm. We need to subtract 1 hour and 40 mins off that time to find out what time she left work. Let’s break the 1 hour and 40 mins into two parts and work with each number. Step 4: 6:10pm – 40 mins = 5:30pm. 5:30pm – 1 hour = 4:30pm Step 5: Isla left work at 4:30pm to leave for her appointment. Step 6: The correct answer is – d) 4:30pm. a) 4:55pm Refer to Explanation of Answer b) 4:45pm Refer to Explanation of Answer c) 4:39pm Refer to Explanation of Answer d) 4:30pm Correct Answer None Question 155. A factory’s management collected data about its work force. It collected that data in two different ways. Use the information from both tables to determine the correct statement. Explanation of answer: Step 1: To find out the correct statement we need to go through each statement a look at their respective details. Step 2: Statement a): Experienced workers have worked for 1 year. We can see on the left hand table that experienced workers have worked for 2 – 4 years. This statement is incorrect. Step 3: Statement b): A level 6 worker is considered a very experienced worker. When looking at the right hand table we can see that a level 6 worker has worked between 4 – 5 years. This links with the table on the left that says very experienced workers have worked for 4+ years. This statement is correct. Step 4: Statement c): A worker with little experience would be a level 4 worker. Looking at the right hand side table we can see that a level 4 worker has 2 – 3 years of experience. This amount of years experience places them as an experienced worker. This statement is incorrect. Step 5: Statement d) A very experienced worker has worked for at least 3 years. Looking at the right hand table we can see that a very experienced worker has worked for 4+ years. This statement is incorrect. Step 6: The correct answer is – b) A level 6 worker is considered a very experienced worker. a) Experienced workers have worked for 1 year Refer to Explanation of Answer b) A level 6 worker is considered a very experienced worker Correct Answer c) A worker with little experience would be a level 4 worker Refer to Explanation of Answer d) A very experienced worker has worked for at least 3 years Refer to Explanation of Answer None Question 156. Two hotels rent out rooms to paying customers. Hotel one charges $1500 for a 7 night stay Hotel two charges ¾ of Hotel one’s price. What is Hotel two’s price for 7 nights? Explanation of answer: Step 1: To answer this question we must first find out what is one quarter of $1500. From there was can work out ¾ of $1500. Step 2: Half of $1500 would be $750. To find half of $750, we should split the number into two parts: $700 and $50. Half of $700 = $350 and Half of $50 is $25. We need to add those two numbers together. $350 + $25 = $375. This is one quarter of $1500. Step 3: If a quarter of $1500 is $375 and a half of $1500 is $750 then we need to add that quarter and half together to get three quarters. We can split the numbers into easier parts to make the addition. $750 becomes $700 and $50. $375 becomes $300 and $75. We can add $700 and $300 to get $1000. Adding $75 and $50 together gives $125. So $1000 add $125 = $1125. Step 4: Hotel two charges $1125 for a 7 night stay. Step 5: The correct answer is – d) $1125. a) $965 Refer to Explanation of Answer b) $1000 Refer to Explanation of Answer c) $1075 Refer to Explanation of Answer d) $1125 Correct Answer None Question 157. Lucas was making a picnic table for his outdoor alfresco area. He was fastening the last nuts and bolts into the table. When fastening one nut, he turned his wrench through 7 half revolutions to tighten the nut. How man degrees did Lucas turn the wrench through? Explanation of answer: Step 1: The question states that the wrench went through 7 half revolutions. One revolution is 360 degrees, so a half revolution would be 180 degrees. We would have to multiply 180 by 7 to find out our answer. Step 2: Let’s break down the number 180 into two parts; 100 and 80. Let’s multiply 100 by 7 = 700. Let’s multiply 80 by 7 = 560. Add 700 and 560 together to give = 1,260 degrees. Alternate Step 2: 180 x 2 = 360 = 1 full revolution. 7 half revolutions is equal to 3 full revolutions and 1 half revolution. 3 x 360 = 1,080 degrees. 1080 + 180 = 1,260 degrees. Step 3: Lucas had to turn the wrench through 1,260 degrees to fasten the nut to the picnic table. Step 4: The correct answer is – c) 1,260 degrees. a) 900 degrees Refer to Explanation of Answer b) 1,080 degrees Refer to Explanation of Answer c) 1,260 degrees Correct Answer d) 1,440 degrees Refer to Explanation of Answer None Question 158. A cricket sight screen is used so a batsman can see the cricket ball clearly as it comes out of a bowler’s hand. Sight screens are rectangular in size, mostly 4 m by 5 m and are placed at the edge of the oval behind the bowler’s run up. What is the area of the 4 m by 5 m sight screen in square centimetres (cm2)? Explanation of answer: Step 1: When working with figures that need conversion it is best to know some base measurements. For example: 1 m by 1 m = 1 m2 and 100 cm x 100 cm = 10,000 cm2. Step 2: In this case we are working with metres and converting into centimetres. As there are 100 centimetres in 1 meter we must convert the original values into centimetres to find out our answer. Step 3: So 4 m = 400 cm and 5 m = 500 cm. To get the answer we must multiply 400 cm by 500 cm. The best way to do this is to remove the 4 zeros off the 400 and 500 and add them onto the end of the answer. For example we multiply 4 by 5 to get 20. We then add those same 4 zeros onto the end of the 20 to give us 200,000. Step 4: This means that 400 cm by 500 cm equals 200,000 cm2. Step 5: The correct answer is – a) 200,000 cm2. a) 200,000 cm2 Correct Answer b) 185,000 cm2 Refer to Explanation of Answer c) 160,000 cm2 Refer to Explanation of Answer d) 144,000 cm2 Refer to Explanation of Answer None Question 159. Brett was selling his boat for $165,000. Three weeks later the price was reduced by $25,000 He ended up selling the boat for 5% less than the reduced price. How much did he sell the boat for? Explanation of answer: Step 1: You need to figure out what the reduced cost would be first. So $165,000 minus $25,000 = $140,000. Step 2: From there you need to figure out what 5% of $140,000 is. 10% of $140,000 = $14,000. 5% is half of 10% so half of $14,000 is $7,000. Step 3: Then we must subtract $7,000 from $140,000. Subtracting $7,000 from $140,000 would be $133,000. So the price Brett sold the boat for was $133,000. Step 4: The correct answer is – b) $133,000 a) $130,000 Refer to Explanation of Answer b) $133,000 Correct Answer c) $135,000 Refer to Explanation of Answer d) $138,000 Refer to Explanation of Answer None Question 160. Jack bought a new iPhone. It has a 128 gigabyte (GB) hard drive. He notices that 5% of the storage space is already used for the iPhone operating system. How much space is left on his new iPhone? Explanation of answer: Step 1: When figuring out the percentage for this question you should first find 10% of the total amount (128 GB). Step 2: To find 10% of 128, we move the decimal point one place value to the left. This will give you 12.8 (If you multiply 12.8 by 10 you would get 128 which is 100% of Jack’s iPhone space). Step 3: Once you have found 10% then you need to find 5% as this is the amount of space used on the iPhone. As 12.8 is 10% of the total we simply divide 12.8 by 2 to get 5% of the total. So 12.8 ÷ 2 = 6.4. This means that 6.4 GB of storage space is already used. Step 4: To find out how much space is left on his new iPhone we need to subtract 6.4 GB (5% of storage space) from 128 GB. As this value has a decimal point let’s split the 6.4 into 6 and 0.4 and subtract each separately. 128 GB – 6 GB = 122 GB and 122 GB – 0.4 GB = 121.6 GB. Step 5: There is 121.6 GB of storage space left on Jack’s new iPhone. Step 5: The correct answer is – d) 121.6 GB. a) 98.9 GB Refer to Explanation of Answer b) 105.6 GB Refer to Explanation of Answer c) 114.2 GB Refer to Explanation of Answer d) 121.6 GB Correct Answer None Question 171. Printing business cards costs $3 for a box of 50 cards. Pia wants to buy 27 boxes of business cards. Which expression states the total cost of the business cards that Pia wants to purchase? The correct expression is: Please select your answer a) 3 x 20 + 7 Refer to Explanation of Answer b) 3 x 20 + 27 Refer to Explanation of Answer c) 3 x 20 + 3 + 7 Refer to Explanation of Answer d) 3 x 20 + 3 x 7 Correct Answer Explanation of answer: Step 1: To answer this question it is worth looking at the expressions displayed in the drop down box. These expressions give us a hint to how we should go about answering the question. Step 2: What the answers are telling us is that the number of 27 has been split into two parts to find the answer. We can see that the 27 has been split into 20 and 7. Both must be multiplied by 3 (dollar value) and added together to give us our answer. The fact that there are 50 cards in a box is not important because we are not being asked to calculate the total number of cards. Step 3: So 3 x 20 and 3 x 7 are the split numbers. We add the + symbol to the middle of the expression to give us the final number. Step 4: Therefore, the expression is 3 x 20 + 3 x 7 Step 5: The correct answer is – d) 3 x 20 + 3 x 7 Question 172. The nutrition information on a flavoured milk carton is shown below: One serving size of the milk contains 19 g of protein. What amount of protein does 1000 mL of milk contain? Explanation of answer: Step 1: The serving size of the carton of flavoured milk is 600 mL, we need to find out how much fat is in 1,000 mL of milk. This means multiplying 600 mL is not going to be a neat operation. Step 2: We know that 600 mL of milk contains 19 grams of protein. If we multiply the 600 mL by 2 then we get 1200 mL of milk, which is too much milk. The difference between 1000 mL and 600 mL is 400 mL. This difference of 400 mL is 2/3rds of the original size. 600 mL + 400 mL = 1000 mL. All we need to do is figure out what is 2/3rds of 19 grams of protein and we can find out the answer. Step 3: To find 2/3rds of 19 grams we need to split the 19 grams into thirds. 18 ÷ 3 = 6 and 1 ÷ 3 = 0.33 So if 1/3rd of 19 is 6 + 0.33 = 6.33, then 2/3rds of 19 must be 2 x 6.33 = 12.66. So 400 mL of milk would have 12.66 grams of protein. Step 4: We now add the totals together. 600 mL contains 19 grams and 400 mL contains 12.66 grams, so 1000 mL (400mL + 600 mL) contains 19 + 12.66 = 31.66 grams of protein. Step 5: The correct answer is – d) 31.66 grams a) 30.50 grams Refer to Explanation of Answer b) 31.66 grams Refer to Explanation of Answer c) 32.33 grams Refer to Explanation of Answer d) 34.66 grams Correct Answer None Question 173. Aaron painted the ceilings of the rooms shown below: How many square metres did he paint? Explanation of answer: Step 1: The easiest way to solve this question is to work out the area of the large rectangle that would go around the outer perimeter of both rooms, and then subtract the small rectangular area that is not part of a room. This simplifies the calculations but if it doesn’t seem intuitive, refer to the alternative explanation below. Step 2: The horizontal dimension of the large outer rectangle is given as 8m. The vertical dimension is 5m + 1m = 6m. We multiply these overall dimensions to work out the area of the large outer rectangle in square metres. 8m x 6m = 48m² Step 3: The vertical dimension of the small rectangle that is not part of a room is given as 1m. The horizontal dimension of this rectangle is 8m – 4.5m = 3.5m. Again we multiply these dimensions to work out the area of the small rectangle in square metres. 1m x 3.5m = 3.5m². Step 4: We must subtract the small area from the large area to find out the total area of the ceiling. 48m² – 3.5m² = 44.5m². Aaron painted 44.5m² of ceiling. Step 5: The correct answer is – a) 44.5m² ALTERNATE Explanation Step 1: To find out how many square metres Aaron had to paint we need to divide the diagram above into two rectangles – one representing each room. Step 2: Before we try to split the diagram up, we are missing two pieces of information. One is the smaller horizontal line on the right-hand side of the diagram (the kitchen). To find this information we need to subtract the bottom horizontal line value (4.5m) from the top horizontal line value (8m). 8m – 4.5m = 3.5m. Step 3: We now need to find the length of the vertical line running down the middle of the diagram. To find this we can add the two lengths on the right hand side of the diagram. This is 5m + 1m = 6m. Step 4: Now we can split the diagram along the vertical line that separates the two rooms. This gives us two rectangles. The smaller rectangle now has two sides with dimensions 5m and 3.5m. To find the area of this rectangle we multiply the 5m by 3.5m. This equals 17.5m2 Step 5: The larger rectangle now has two sides with dimensions 6m and 4.5m. To find the area of this rectangle we multiply the 6m by 4.5m. This equals 27m2 Step 6: We add the areas of both rectangles to find our answer. So 17.5m2 + 27m2 = 44.5m2 Step 7: The correct answer is – a) 44.5m2 a) 44.5m2 Correct Answer b) 41m2 Refer to Explanation of Answer c) 39.5m2 Refer to Explanation of Answer d) 38m2 Refer to Explanation of Answer None Question 174. Over the last few years Matt averaged his expenditures on his car: These were: On average, how much did he spend on his car each year? Explanation of answer: Step 1: As we can see from the table Matt has different time frames for how much he spends on his car. The question asks how much does he spend on his car over a year. We need to put all these values into a yearly total. Step 2: The car licence ($620) and service and repairs ($440) are already in a yearly total, so we don’t need to change these totals. Step 3: The petrol cost ($20 per week) needs to be changed. We multiply the $20 by 52 (as there are 52 weeks in a year), so $20 x 52 = $1,040. You can break this up to make it easier to work out: 20 x 52 = 2 x 10 x 52 = 104 x 10 = 1,040. Step 4: The insurance cost ($50 per month) also needs to be changed. We multiply the $50 by 12 (as there are 12 months in a year), so $50 x 12 = $600. Again, you can break this up to make it easier to work out: 50 x 12 = 5 x 10 x 12 = 60 x 10 = 600 Step 5: To find our answer we must add all these totals together. So, $620 + $440 + $1,040 + $600 = $2,700 Step 6: The correct answer is – b) $2,700 a) $2,650 Refer to Explanation of Answer b) $2,700 Correct Answer c) $2,780 Refer to Explanation of Answer d) $2,800 Refer to Explanation of Answer None Question 175. Grant has a water container that is 40cm high, 50cm wide and 60cm long. The surface of the water is 10 cm from the top of the container. If Grant wants to fill 2-litre water bottles for his friends to use on a hiking trip, how many bottles will he be able to fill using the water in the container? Explanation of answer: Step 1: This question requires us to first work out the volume of water in the container and then how many 2 litre bottles can be filled with that volume. Step 2: We are given the length and width of the container, but remember that the depth of the water is 10 cm less that the height of the container. So the depth of the water is 40 cm – 10 cm = 30 cm. Step 3: To find the volume of the water in the container we must multiply 60 cm x 50 cm x 30 cm. To simplify this calculation we can break it up as follows: 60 x 50 x 30 = 6 x 5 x 3 x 10 x 10 x 10 = 30 x 3 x 1000 = 90 x 1000 = 90,000. So the volume of water is 90,000 cm³ Step 4: One cubic centimetre (1 cm³) is the same as one millilitre (1 ml). There are 1000 millilitres in a litre, so to find out how many litres are in the container we need to divide 90,000 by 1,000. 90,000 cm3 ÷ 1,000 = 90,000 ml = 90,000 ml ÷ 1,000 = 90 litres. There are 90 litres of water in the container. Step 5: Now we need to divide the 90 litres by 2 as we are trying to fill 2-litre bottles. 90 ÷ 2 = 45, so Grant would be able to fill 45, 2-litre bottles using the water in the container. Step 5: The correct answer is – a) 45 bottles a) 45 bottles Correct Answer b) 43 bottles Refer to Explanation of Answer c) 38 bottles Refer to Explanation of Answer d) 35 bottles Refer to Explanation of Answer None Question 176. Before slikpik, lotto players had to choose six numbers from 1 to 45. To win the lotto jackpot, they had to have all six numbers corresponding to the lotto draw. Charlotte’s numbers were: 16, 17, 25, 27, 36, 42 Matilda’s numbers were: 15, 20, 25, 30, 35, 45 Olivia’s numbers were: 9, 13, 21, 28, 41, 45 Which one of these statements is true? Explanation of answer: Step 1: Whenever reading a question on chance like this one, it is important to understand that in any chance event that requires a random selection of numbers, every person involved in that chance event has an equal chance of winning. Regardless of which numbers a person chose or how they chose them, each number has the same probability of being drawn in the lotto. Step 2: So in this question all three players have the same chance of winning. Step 3: The correct answer is – d) All three players have the same chance of winning. a) Olivia’s numbers are completely random, so she is the most likely to win. Refer to Explanation of Answer b) Charlotte’s numbers are large, and hence have the best chance of winning. Refer to Explanation of Answer c) All three players have the same chance of winning. Refer to Explanation of Answer d) Matilda’s numbers have a pattern, so she has the least chance of winning. Correct Answer None Question 177. A map of Perth Airport’s runway network has a scale of 1 : 50,000 On the map, the length of the main runway is 7 centimetres. What is the actual length of the main runway? Explanation of answer: Step 1: The way to figure out the length of the runway is to use the scale ratio mentioned in the first sentence. The scale ratio says that 1 cm on the map is equivalent to 50,000 cm on the ground. Step 2: We need to multiply the length of the runway on the map (7 cm) by the scale ratio of 50,000. We can remove the three zeros to make the multiplication easier. 7 x 50 = 350. Bring back the three zeros to the total to make 350,000. This means the runway is actually 350,000 cm long. Step 3: There are 100 centimetres in a metre, so to convert 350,000 cm into metres we need to divide it by 100. This is simply done by dropping two zeros: 350,000 ÷ 100 = 3,500. So according to the map, the runway at Perth Airport is actually 3,500 metres long. Step 4: The correct answer is – b) 3,500 m. a) 4,000 metres Refer to Explanation of Answer b) 3,500 metres Correct Answer c) 3,250 metres Refer to Explanation of Answer d) 3,000 metres Refer to Explanation of Answer None Question 178. Tom found an old soup recipe that required him to use 4 pints of chicken stock and 2 pints of water in the soup. A pint measures 568 millilitres in volume. If Tom doesn’t add any other ingredients, what is the closest amount of soup that the recipe makes in litres? Explanation of answer: Step 1: This question is basically asking us covert millilitres to litres. We have 4 pints of chicken stock and 2 pints of water, giving us a total of 6 pints of fluid in the soup. We now need to multiply the 6 pints by the volume of the pint (568 mL). The question asks what is closest amount of soup made from the recipe. This says that we should have an approximate value from our calculations. Step 2: To make the calculation easier we can round the volume of a pint from 568 mL up to 570 mL. Note that since we are only working with 6 pints, this rounding up will only increase our answer by 6 x 2 mL = 12 mL, which is the same as 0.012 litres – a very small inaccuracy. Step 3: We need to multiply the 570 by 6. Break apart the 570 into two parts. 500 and 70. 500 mL x 6 = 3,000 mL and 70 mL x 6 = 420 mL. Add the two totals together 3,000 mL + 420 mL = 3,420 mL. Step 3: Divide by 1,000 to convert the 3,420 mL to litres. 3,420 mL ÷ 1,000 = 3.42 litres. This becomes 3.4 litres if we round to one decimal place. Step 4: The correct answer is – c) 3.4 litres a) 3.8 litres Refer to Explanation of Answer b) 3.5 litres Refer to Explanation of Answer c) 3.4 litres Correct Answer d) 3.1 litres Refer to Explanation of Answer None Question 179. The middle triangle that is formed in this roof truss is an isosceles triangle. What is the size of the angle labelled x? Explanation of answer: Step 1: The first piece of information that we need to know, is the characteristics of an isosceles triangle. An isosceles triangle has two sides and two angles that are the same. In this instance the two sides that would be same are the sides coming from the apex of the roof. That means the two angles that are the same, are the bottom two angles. Step 2: To find the value of x we also need to know that the interior angles of a triangle add up to 180°. This requires us to subtract the total value of the bottom two angles from 180° to give the value of x. Step 3: If the bottom two angles are the same, we can calculate the total size of the two angles at the bottom of the triangle. This would be 72° x 2 = 144°. Step 4: All that is required now is to subtract 144° from 180° to find the value of x. 180° – 144° = 36°. Step 5: The correct answer is – b) 36°. a) 23° Refer to Explanation of Answer b) 36° Correct Answer c) 42° Refer to Explanation of Answer d) 48° Refer to Explanation of Answer None Question 180. On a real estate website, the median sales price for a house in the suburb of Hill Valley was $450,000. During the last month 37 houses were sold, including one for $1.5 million. If the $1.5 million house is not included in the calculation of the median price, which statement would be true? Explanation of answer: Step 1: In statistical analysis the median is known as the “middle” number in a numerically ordered data set. Removing a number from the data set could change the median value because the number in the middle of the old set is no longer in the middle of the new set. However, the median number could also stay the same if there are multiple numbers in the remaining set that are the same as the original median number. Step 2: If we take out the sale of the $1.5 million house from the data range, we could find that the median house price decreases because we have removed a number that was higher than the original median i.e. the original median is now positioned just above the new median. Note that if we take one number away from a set of 37 numbers, then we are left with 36 numbers. Since 36 is even, there is no middle number. In this case the mean is calculated as being the average of the two middle numbers in the set. So the new median could be lower, but it cannot be higher. Step 3: As we don’t know the data set, we don’t know if it contains several numbers that are the same as the original median price. This means the new median price could remain the same. Step 4: This gives us our answer that the median price must either stay the same or be lower. Step 5: The correct answer is – a) The median price must either stay the same or be lower. a) The median must either stay the same or be lower. Correct Answer b) The median must either stay the same or be higher. Refer to Explanation of Answer c) The median must stay the same. Refer to Explanation of Answer d) The median must be lower. Refer to Explanation of Answer None You’ve already answered some of the questions! Would you like to continue with quiz or restart it from beginning? Time's up Submit a CommentYour email address will not be published. Required fields are marked *Comment * Name Email Website Δ
