Scales, Maps and Rates #1

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Numeracy (Questions 191 – 200)

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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 191.

Sally bought a new Hybrid car for its fuel efficiency.

On average her car uses 6 L per 100 km.

Last week Sally drove a total of 354 km.

The amount of fuel her car used last week is closest to:

Explanation of answer:

Step 1: If a car uses 6 L per 100 km, then for every subsequent 100 km travelled we should add another 6 L of fuel used. For example, 100 km = 6 L, 200 km = 12 L.

Step 2: The question states that Sally drove 354 km in a week. If we continue to use the same formula as above, then 300 km = 18 L used.

Step 3: As 54 km is roughly half of 100 km, then we can assume that she would use approximately half of the fuel required to drive 100 km. Half of 6 L is 3 L. Now all we have to do is add the 18 L + 3 L = 21 L

Step 4: Sally’s car has used approximately 21 L in driving 354 km last week.

Step 5: The correct answer is – b) 21 L

a) 18 L Refer to Explanation of Answer

b) 21 L Correct Answer

c) 24 L Refer to Explanation of Answer

d) 27 L Refer to Explanation of Answer

None

Question 192.

A personal trainer was instructing a client on how to perform a squat.

In those instructions it was said that the angle behind the knee joint should be small to achieve a deep squat.

Which of the following best describes the angle formed behind the knee joint in this picture?

Explanation of answer:

Step 1: A right angle should be at exactly 90°, the knee angle above is less than 90°.

Step 2: An obtuse angle is more than 90° and less than 180°, the knee angle above is less than that range.

Step 3: A reflex angle is more than 180° but less than 360°, again, the knee angle above is less than that range.

Step 4: An acute angle is less than 90°, the knee angle above matches this description and is the correct answer.

Step 5: The correct answer is – d) Acute angle

a) Right angle Refer to Explanation of Answer

b) Obtuse angle Refer to Explanation of Answer

c) Reflex angle Refer to Explanation of Answer

d) Acute angle Correct Answer

None

Question 193.

Asha has a gift-wrapping business that uses many different coloured ribbons when wrapping presents.

For one job, she needed 8 different coloured ribbons, each 5,500 mm long.

The cost of the ribbon is $2 per metre, how much did Asha pay?

Explanation of answer:

Step 1: We know that Asha needs 8 different types of ribbon. We will need to use this number as a multiplication later in our calculation.

Step 2: The ribbon is charged at $2 per metre. She buys ribbon in lengths of 5,500 mm. We need to covert that figure into metres. 1,000 mm = 1 m, so 5,500 mm = 5.5 m.

Step 3: We need to multiply \$2 by 5.5 m to get the cost of one ribbon. 2 x \$5.5 = \$11. One ribbon costs \$11.

Step 4: Since Asha has 8 ribbons, we need to multiply the 8 ribbons by \$11. 8 x \$11 = \$88

Step 5: The correct answer is – b) $88

a) $44 Refer to Explanation of Answer

b) $88 Correct Answer

c) $440 Refer to Explanation of Answer

d) $880 Refer to Explanation of Answer

None

Question 194.

Kayden owns a two-bedroom townhouse which has the following plan.

The unit has exterior and interior doors.

Excluding the garage door and cupboard doors, what is the total number of doors in Kayden’s plan?

Explanation of answer:

Step 1: The only way to answer this question is to count the number of doors on the plan.

Step 2: There is 1 door between the kitchen and garage, and 1 door to the pantry. There are 2 doors to the bathroom and laundry, 2 doors from the master bedroom to the walk-in-closet, 1 door to the master bedroom, 2 doors in bedroom 2 and 1 door to the porch.

Step 3: When we add all the doors together, we get 10 doors.

Step 4: The correct answer is – a) 10

a) 10 Correct Answer

b) 9 Refer to Explanation of Answer

c) 8 Refer to Explanation of Answer

d) 7 Refer to Explanation of Answer

None

Question 195.

Mercy was looking at the Australian Bureau of Statistics website and noticed that almost 500,000 people regularly took the train to work. Out of the total population that uses some type of transport to work, this equals 5% of the Australian population traveling to a workplace.

What is 5% expressed as a fraction?

Explanation of answer:

Step 1: In answering this question we need to know what a percentage is expressed as a fraction.

Step 2: 50% is expressed as ⁵⁰⁄₁₀₀ which is the same as ⁵⁄₁₀, 10% is expressed as ¹⁰⁄₁₀₀ which is the same as ¹⁄₁₀, and 1% is expressed as ¹⁄₁₀₀.

Step 3: 5% is therefore expressed as ⁵⁄₁₀₀.

Step 4: The correct answer is – c) ⁵⁄₁₀₀

a) ⁵⁄₁₀ Refer to Explanation of Answer

b) ¹⁄₅ Refer to Explanation of Answer

c) ⁵⁄₁₀₀ Correct Answer

d) ¹⁄₅₀ Refer to Explanation of Answer

None

Question 196.

An ice cream shop collected some data of people’s favourite ice cream purchases. The graph below shows the data they collected.

Which of the following statements is NOT true?

Explanation of answer:

Step 1: The question asks us to find the answer that is NOT true. So, we must go through all the answers to see which one is not true.

Step 2: a) “Just less than half of the people chose Cookies and Cream or Vanilla as their favourite ice cream” – This statement is true as the combined Vanilla and Cookies and Cream chart area is just less than half of the full area of the chart.

Step 3: b) “Cookies and Cream was less popular than Vanilla” – This statement is NOT true, as the chart area for Cookies and Cream was larger than the chart area for Vanilla, making it MORE popular.

Step 4: c) “Mint Choc Chip was the most popular ice cream” – This statement is true as the chart area for Mint Choc Chip is the largest of all the flavours.

Step 5: d) “More people chose Chocolate, than Strawberry, as their favourite ice cream” – This statement is true as the chart area for Chocolate is larger than the chart area for Strawberry.

Step 6) Going through these answers shows us that answer b) is the statement that is NOT true.

Step 6: The correct answer is – b) Cookies and Cream was less popular than Vanilla

a) Just less than half of the people chose Cookies and Cream or Vanilla as their favourite ice cream Refer to Explanation of Answer

b) Cookies and Cream was less popular than Vanilla Correct Answer

c) Mint Choc Chip was the most popular ice cream Refer to Explanation of Answer

d) More people chose chocolate, than Strawberry, as their favourite ice cream Refer to Explanation of Answer

None

Question 197.

Wyatt and Anton are playing a game of Battleship, a grid guessing game.

Anton has set up his ships in the format below. Wyatt has the first turn and calls out the first grid location of (E, 5) which is a miss.

On Wyatt’s second turn he calls out the next grid location of (C, 7). What ship does he hit?

Explanation of answer:

Step 1: The way to answer this question is to make sure you read the grid reference and ship key correctly.

Step 2: The grid reference of (C, 7) must be read in that order. Find the letter “C” on the left-hand side of the grid then track along that row until you find the number ”7” along the top columns. This grid reference indicates that a ship has been hit.

Step 3: This ship is a 5-hole ship, so when looking at the key on the right, this would indicate that the Carrier was hit.

Step 4: The correct answer is – a) Carrier

a) Carrier Correct Answer

b) Battleship Refer to Explanation of Answer

c) Submarine Refer to Explanation of Answer

d) Patrol Boat Refer to Explanation of Answer

None

Question 198.

Meadow’s family owns a pet pig. When they bought the pig, it weighed 30.3 kg. They weighed the pig two weeks later. It weighed 31.2 kg

How many grams did the pig gain over the two weeks?

Explanation of answer:

Step 1: We need to find the difference between the initial weight and the last recorded weight of the pig to find our answer.

Step 2: The initial weight was 30.3 kg. The latest recorded weight was 31.2 kg. To find the difference we subtract 30.3 kg from 31.2 kg. To make this easier we can remove the 30 kg from each total to find the difference. Doing this gives us: 1.2 kg and 0.3 kg. 1.2 kg – 0.3 kg = 0.9 kg.

Step 3: Even though we have found the answer, we need to convert to grams as this is what the question requires as an answer. We need to convert 0.9kg into grams. 1,000 g is 1 kg, 500 g is 0.5 kg and 100 g is 0.1 kg. So, 900 g is 0.9 kg.

Step 4: The correct answer is – c) 900 g

Question 199.

Peter owns a self-storage facility in an industrial area. He is creating new units that have floor dimensions of 3 m by 3 m. The total floor space available for storage units is 540 m²

What is the largest number of units he can create?

Explanation of answer:

Step 1: First we need to calculate the floor area (number of m²) of each unit. We are told the unit dimensions are 3 m by 3 m. 3 x 3 is 9, so we have 9 m² of floor space per unit.

Step 2: Peter has a total of 540m² floor space to create these units. We need to divide that total floor space by the space of one unit. So, 540m² divided by 9m². We can make this calculation a bit easier by dropping the zero from the 540 then adding it onto the end of the answer. 54 ÷ 9 = 6. We add the zero on the end of the 6 to give 60.

Step 3: We have found that Peter can create 60 units of storage from his total of 540m² of floor space.

Step 4: The correct answer is – a) 60

a) 60 Correct Answer

b) 54 Refer to Explanation of Answer

c) 36 Refer to Explanation of Answer

d) 27 Refer to Explanation of Answer

None

Question 200.

This picture is from a car fuel gauge. This gauge shows how much petrol is left in the petrol tank.

The tank can hold 60 litres of petrol when full.

Estimate how much fuel is left in the petrol tank.

Explanation of answer:

Step 1: To find the answer for this question, we must understand that a fuel gauge is divided into quarters. In this picture the needle is pointing to the last quarter (before empty) mark. This would be represented as ¹⁄₄ as a fraction.

Step 2: The tank holds 60 Litres of petrol. A quarter can be found by halving a half. So, a half of 60 is 30 and a half of 30 is 15. So, the volume of fuel remaining in the tank is equal to ¹⁄₄ of the total tank volume, and this is 15 Litres.

Step 3: The correct answer is – d) 15 L

a) 60 L Refer to Explanation of Answer

b) 45 L Refer to Explanation of Answer

c) 30 L Refer to Explanation of Answer

d) 15 L Correct Answer

None

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Numeracy (Questions 181 – 190)

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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 181.

It costs $2.10 to send a 50 g letter from Australia to New Zealand.

Select the stamps that would be found on the envelope.

Explanation of answer:

Step 1: The question states that it costs \$2.10 to send a letter from Australia to New Zealand. You need to find out which three stamps were used on the letter to make \$2.10. You will need to add the prices on the stamps to find the total.

Step 2: Add items A, B & D together. 60c + \$1 + 70c = \$2.30. Not the correct answer.

Step 3: Add items B, C & D together. \$1 + 50c + 70c = \$2.20. Not the correct answer.

Step 4: Add items A, C & D together. 60c + 50c + 70c = $1.80. Not the correct answer.

Step 5: Add items A, B & C together. 60c + \$1 + 50c = \$2.10. The correct answer.

Step 6: There are other combinations that will give a total of \$2.10 (e.g. C + C + C + A = 50c + 50c + 50c + 60c = \$2.10, or D + D + D = 70c + 70c + 70c = $2.10.), but to answer this question we only need to consider the combinations a), b), c) and d) provided as possible answers. Since there are four different stamp combinations to consider, this question requires a process of elimination to determine the correct answer. This process is shown above.

Step 7: The correct answer is – d) A, B & C.

a) A, B & D Refer to Explanation of Answer

b) B, C & D Refer to Explanation of Answer

c) A, C & D Refer to Explanation of Answer

d) A, B & C Correct Answer

None

Question 182.

This tally chart shows the essay results of students in an English class.

A mark of 27 or more is considered to be a good mark.

How many students received a good mark?

Explanation of answer:

Step 1: When reading this tally chart every stroke represents one student. The question tells us that a mark of 27 or more is considered a good mark. This means we need to count all the students who scored 27 or more.

Step 2: Count the students that received 27 marks: 4

Step 3: Then count the students who received 28, 29 and 30 marks: 5, 0, 2

Step 4: Add those totals: 4 + 5 + 0 + 2 = 11

Step 5: There are 11 students who have received 27 marks or more for their English essay.

Step 6: The correct answer is – b) 11.

a) 9 Refer to Explanation of Answer

b) 11 Correct Answer

c) 12 Refer to Explanation of Answer

d) 14 Refer to Explanation of Answer

None

Question 183.

A whale shark tour company in Ningaloo offers full day whale shark tours for tourists.

Which expression gives the correct total cost in dollars, for 2 adults and 3 children of ages 8, 9 and 11 years?

Explanation of answer:

Step 1: To complete this answer you must understand how the order of operations acronym BIMDAS (brackets, indices, multiplication, division, addition and subtraction) works. You don’t actually need to calculate an answer, but you will need to know how BIMDAS works.

Step 2: The main concept in this question is knowing what the figures within the brackets mean. The single digit number is the number of people and the larger number is the cost. We need to match the number of people and cost in the choices presented, to what the question asked us. The Whale Shark Tour has 2 adults and 3 children attending.

Step 3: Looking at the answers given, we should look to see if the numbers presented to us are correct. Let’s go through each answer.

Step 4: a) (2 x 350) + 280 : Inside the brackets the 2 represents 2 adults and the 350 represents the cost for each adult, however, having only one cost of 280, means that there is only one child attending. This doesn’t match the question. This is not the correct answer.

Step 5: b) (2 x 350) + (3 x 280) : Inside the first brackets the 2 represents 2 adults and the 350 represents the cost for each adult. Inside the second brackets the 3 represents 3 children and the 280 represents the cost for each child. This means there are 2 adults and 3 children going on the tour. This does match the question. This is the correct answer.

Step 6: c) (5 x 350) + (5 x 280) : Inside the first brackets the 5 represents 5 adults and the 350 represents the cost for each adult. Inside the second brackets the 5 represents 5 children and the 280 represents the cost for each child. This means there are 5 adults and 5 children going on the tour. This doesn’t match the question. This is not the correct answer.

Step 7: d) (2 x 350) + (3 x 310) : Inside the first brackets the 2 represents 2 adults because the cost is \$350 each. Inside the second brackets the 3 represents 3 seniors because the cost is \$310 each. This means there are 2 adults and 3 seniors going on the tour. This does not match the question. This is not the correct answer.

Step 8: The correct answer is – b) (2 x 350) + (3 x 280)

a) (2 x 350) + 280 Refer to Explanation of Answer

b) (2 x 350) + (3 x 280) Correct Answer

c) (5 x 350) + (5 x 280) Refer to Explanation of Answer

d) (2 x 350) + (3 x 310) Refer to Explanation of Answer

None

Question 184.

Evie has a recipe for 2 servings of Malaysian chicken Mie Goreng.

She wants to make just one serving for herself.

How many grams of dried egg noodles would Evie need?

Explanation of answer:

Step 1: When reading this question there are 2 important pieces of information that you must use to find the answer. The first is that the recipe is for 2 servings, the second is that Evie only wants to make 1 serving. Essentially, she wants to halve the recipe for herself.

Step 2: Since we know Evie wants to halve the recipe, the next part of the question asks us how many grams of dried egg noodles she would need. We need to halve the amount of dried egg noodles to get the answer.

Step 3: The recipe uses 150 g of egg noodles. Divide 150 by 2 to get the answer. 150 g ÷ 2 = 75 g

Step 4: Alternatively, split 150 g into 140 g and 10 g and divide both by 2. 140 g ÷ 2 = 70 g, 10 g ÷ 2 = 5 g. 70 g + 5 g =75 g

Step 5: The correct answer is – a) 75 g.

a) 75 g Correct Answer

b) 100 g Refer to Explanation of Answer

c) 225 g Refer to Explanation of Answer

d) 300 g Refer to Explanation of Answer

None

Question 185.

A survey of 100 people was taken at a bakery. Those 100 people were asked to give a response to the following question: “Do you like chocolate muffins?”

- 60% of the people surveyed said “yes”

- ¹⁄₅ of the people surveyed said “no”

- The rest of the people surveyed said “sometimes”

How many people surveyed said “no” to the question?

Explanation of answer:

Step 1: We are asked how many people said “no” to the question. This requires you use the fraction given on the second dot point and apply that fraction to the whole number given.

Step 2: In this case the fraction is ¹⁄₅ and the whole number is 100.

Step 3: ¹⁄₅ is the same as saying 20% and 20% of 100 is 20. Alternatively, consider that you want to work out one fifth of the people surveyed. One fifth of 100 can be written as:

¹/₅ x 100

which is the same as:

¹⁰⁰⁄₅ = 20

Step 4: There were 20 people surveyed who answered “no” to the question asked.

Step 5: The correct answer is – d) 20.

a) 60 Refer to Explanation of Answer

b) 30 Refer to Explanation of Answer

c) 25 Refer to Explanation of Answer

d) 20 Correct Answer

None

Question 186.

What is the temperature shown on this thermometer?

Explanation of answer:

Step 1: Looking at the thermometer we can see the notations on the right increase in increments of 10. The answers are all given in degrees Celsius, so this means we are looking at a thermometer measuring in degrees Celsius and increasing in “major increments” of 10 °C.

Step 2: We can also see that between the major increments there are small lines that indicate “minor increments” in temperature. If we look between the 20 °C and 30 °C line, we can see that there are 4 smaller lines. Each of these 4 lines indicates an increase of 2 °C on the thermometer. So, for example, if the red fluid column lined up with the small line above the 20 °C mark, it would indicate a temperature reading of 22 °C.

Step 3: The red fluid in this thermometer indicates the temperature in degrees Celsius – the higher the fluid column, the hotter the temperature. In this case the red fluid column ends below the 20 °C line. We can see that it ends in line with the smaller line below the 20 °C mark. If the smaller line indicates a difference of 2 °C, then we must subtract 2 °C from the 20 °C mark to give us our answer.

Step 4: 20 °C – 2 °C = 18 °C

Step 5: The correct answer is – c) 18 °C

a) 20 °C Refer to Explanation of Answer

b) 19 °C Refer to Explanation of Answer

c) 18 °C Correct Answer

d) 16 °C Refer to Explanation of Answer

None

Question 187.

A department store offers birthday voucher discounts to its store members.

Kat wanted to use her voucher to get 20% off the price of a new coat.

The full price of the coat was $260.

How much will Kat save by using the voucher?

Explanation of answer:

Step 1: To find out how much Kat saved by using the 20% discount voucher, we must be able to manipulate percentages to find that answer.

Step 2: The starting point is to find 10% of \$260. To find this, we move the decimal place one place to the left (This is 10% of \$260). This gives us $26.

Step 3: Now to find 20% we simply double \$26 (since 20% is twice as much as 10%). \$26 x 2 = $52.

Step 4: Kat saved $52 on buying her new coat.

Step 5: The correct answer is – b) $52

a) $64 Refer to Explanation of Answer

b) $52 Correct Answer

c) $48 Refer to Explanation of Answer

d) $41 Refer to Explanation of Answer

None

Question 188.

The forecast for Bunbury indicates there is a 70% chance of rain on Thursday.

Which of the following best describes the likelihood of rain on Thursday?

Explanation of answer:

Step 1: To answer this question we need to understand what a percentage means as a chance event. The closer the percentage is to 100% the higher the chance of that event occurring. The closer to 0% the lower the chance of that event occurring.

Step 2: The question states that the chance of rain is 70%. Included in the picture text it states a “High (70%) chance of rain.” These figures and statements should tell us that there is a high or likely chance of rain.

Step 3: When looking at the answers, we know that the options of “Unlikely” and “Even Chance” are not viable options as an answer. Certain would indicate a 100% chance of rain. The option “Likely” is very similar in nature to the statement: “A high chance of rain (70%)”

Step 4: This would indicate: d) Likely, as the most appropriate answer.

Step 5: The correct answer is – d) Likely

a) Unlikely Refer to Explanation of Answer

b) Even chance Refer to Explanation of Answer

c) Certain Refer to Explanation of Answer

d) Likely Correct Answer

None

Question 189.

Carlos went to watch a Queen tribute band at the Sydney Opera House.

The performance was an afternoon session and started at 3.02pm

The watch face below shows the time the performance finished.

How long did the concert go for?

Explanation of answer:

Step 1: The time on the watch face is 5:22pm. The question states that the concert started at 3:02pm. We need to find out how many minutes the concert went for.

Step 2: We should break up the times to make the calculation easier. The difference between 3:02pm and 5:02pm is exactly 2 hours, which is 120 minutes.

Step 3: The difference from 5:02pm to 5:22pm is 20 minutes.

Step 4: We now add the 120 minutes and 20 minutes together to get our answer. 120 mins + 20 mins = 140 mins. The performance went for 140 minutes.

Step 5: The correct answer is – c) 140 minutes

a) 90 minutes Refer to Explanation of Answer

b) 110 minutes Refer to Explanation of Answer

c) 140 minutes Correct Answer

d) 170 minutes Refer to Explanation of Answer

None

Question 190.

A recreation camp site offers camp accommodation to school groups.

They have 12 beds in each of their rooms

If a school has 81 students staying at the campsite, what is the least number of rooms needed so that every student has a bed?

Explanation of answer:

Step 1: The quickest way to answer this question, is to use the 12 times tables to find out how many rooms are required. We need to get an answer above 81 to determine the number of rooms.

Step 2: In looking at the answers provided, let’s do the math: 12 x 5 = 60, 12 x 6 = 72, 12 x 7 = 84 and 12 x 8 = 96.

Step 3: We can see that 12 x 7 = 84. This is more that the required 81 beds needed, and the least amount of rooms needed for the 81 students.

Step 4: This means that 7 rooms are required to accommodate 81 students (with 3 beds left empty).

Step 5: The correct answer is – c) 7

a) 5 Refer to Explanation of Answer

b) 6 Refer to Explanation of Answer

c) 7 Correct Answer

d) 8 Refer to Explanation of Answer

None

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