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?