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!

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Question 171.

Printing business cards costs $3 for a box of 50 cards.

Pia wants to buy 27 boxes of business cards.

Which expression states the total cost of the business cards that Pia wants to purchase?

The correct expression is:

Explanation of answer:

Step 1: To answer this question it is worth looking at the expressions displayed in the drop down box. These expressions give us a hint to how we should go about answering the question.

Step 2: What the answers are telling us is that the number of 27 has been split into two parts to find the answer. We can see that the 27 has been split into 20 and 7. Both must be multiplied by 3 (dollar value) and added together to give us our answer. The fact that there are 50 cards in a box is not important because we are not being asked to calculate the total number of cards.

Step 3: So 3 x 20 and 3 x 7 are the split numbers. We add the + symbol to the middle of the expression to give us the final number.

Step 4: Therefore, the expression is 3 x 20 + 3 x 7

Step 5: The correct answer is – d) 3 x 20 + 3 x 7

Question 172.

The nutrition information on a flavoured milk carton is shown below:

One serving size of the milk contains 19 g of protein. What amount of protein does 1000 mL of milk contain?

Explanation of answer:

Step 1: The serving size of the carton of flavoured milk is 600 mL, we need to find out how much fat is in 1,000 mL of milk. This means multiplying 600 mL is not going to be a neat operation.

Step 2: We know that 600 mL of milk contains 19 grams of protein. If we multiply the 600 mL by 2 then we get 1,200 mL of milk, which is too much milk. The difference between 1,000 mL and 600 mL is 400 mL. This difference of 400 mL is ²/₃ of the original size. 600 mL + 400 mL = 1,000 mL. All we need to do is figure out what is ²/₃ of 19 grams of protein and we can find out the answer.

Step 3: To find ²/₃ of 19 grams we need to split the 19 grams into thirds.

18 ÷ 3 = 6 and 1 ÷ 3 = 0.33

So if ¹/₃ of 19 is 6 + 0.33 = 6.33, then ²/₃ of 19 must be 2 x 6.33 = 12.66. So 400 mL of milk would have 12.66 grams of protein.

Step 4: We now add the totals together.

600 mL contains 19 grams and 400 mL contains 12.66 grams, so 1,000 mL (400mL + 600 mL) contains 19 + 12.66 = 31.66 grams of protein.

Step 5: The correct answer is – b) 31.66 grams

a) 30.50 grams Refer to Explanation of Answer

b) 31.66 grams Refer to Explanation of Answer

c) 32.33 grams Refer to Explanation of Answer

d) 34.66 grams Correct Answer

None

Question 173.

Aaron painted the ceilings of the rooms shown below:

How many square metres did he paint?

Explanation of answer:

Step 1: The easiest way to solve this question is to work out the area of the large rectangle that would go around the outer perimeter of both rooms, and then subtract the small rectangular area that is not part of a room. This simplifies the calculations but if it doesn’t seem intuitive, refer to the alternative explanation below.

Step 2: The horizontal dimension of the large outer rectangle is given as 8m. The vertical dimension is 5m + 1m = 6m. We multiply these overall dimensions to work out the area of the large outer rectangle in square metres. 8m x 6m = 48m²

Step 3: The vertical dimension of the small rectangle that is not part of a room is given as 1m. The horizontal dimension of this rectangle is 8m – 4.5m = 3.5m. Again we multiply these dimensions to work out the area of the small rectangle in square metres. 1m x 3.5m = 3.5m².

Step 4: We must subtract the small area from the large area to find out the total area of the ceiling. 48m² – 3.5m² = 44.5m². Aaron painted 44.5m² of ceiling.

Step 5: The correct answer is – a) 44.5m²

ALTERNATE Explanation

Step 1: To find out how many square metres Aaron had to paint we need to divide the diagram above into two rectangles – one representing each room.

Step 2: Before we try to split the diagram up, we are missing two pieces of information. One is the smaller horizontal line on the right-hand side of the diagram (the kitchen). To find this information we need to subtract the bottom horizontal line value (4.5m) from the top horizontal line value (8m). 8m – 4.5m = 3.5m.

Step 3: We now need to find the length of the vertical line running down the middle of the diagram. To find this we can add the two lengths on the right hand side of the diagram. This is 5m + 1m = 6m.

Step 4: Now we can split the diagram along the vertical line that separates the two rooms. This gives us two rectangles. The smaller rectangle now has two sides with dimensions 5m and 3.5m. To find the area of this rectangle we multiply the 5m by 3.5m. This equals 17.5m²

Step 5: The larger rectangle now has two sides with dimensions 6m and 4.5m. To find the area of this rectangle we multiply the 6m by 4.5m. This equals 27m²

Step 6: We add the areas of both rectangles to find our answer. So 17.5m² + 27m² = 44.5m²

Step 7: The correct answer is – a) 44.5m²

a) 44.5m^{2^{Correct Answer}}

b) 41m^{2^{Refer to Explanation of Answer}}

c) 39.5m^{2^{Refer to Explanation of Answer}}

d) 38m^{2^{Refer to Explanation of Answer}}

None

Question 174.

Over the last few years Matt averaged his expenditures on his car: These were:

On average, how much did he spend on his car each year?

Explanation of answer:

Step 1: As we can see from the table Matt has different time frames for how much he spends on his car. The question asks how much does he spend on his car over a year. We need to put all these values into a yearly total.

Step 2: The car licence (\$620) and service and repairs (\$440) are already in a yearly total, so we don’t need to change these totals.

Step 3: The petrol cost (\$20 per week) needs to be changed. We multiply the $20 by 52 (as there are 52 weeks in a year), so \$20 x 52 = \$1,040. You can break this up to make it easier to work out: 20 x 52 = 2 x 10 x 52 = 104 x 10 = 1,040.

Step 4: The insurance cost (\$50 per month) also needs to be changed. We multiply the \$50 by 12 (as there are 12 months in a year), so \$50 x 12 = \$600. Again, you can break this up to make it easier to work out: 50 x 12 = 5 x 10 x 12 = 60 x 10 = 600

Step 5: To find our answer we must add all these totals together. So, \$620 + \$440 + \$1,040 + \$600 = \$2,700

Step 6: The correct answer is – b) $2,700

a) $2,650 Refer to Explanation of Answer

b) $2,700 Correct Answer

c) $2,780 Refer to Explanation of Answer

d) $2,800 Refer to Explanation of Answer

None

Question 175.

Grant has a water container that is 40cm high, 50cm wide and 60cm long.

The surface of the water is 10 cm from the top of the container.

If Grant wants to fill 2-litre water bottles for his friends to use on a hiking trip, how many bottles will he be able to fill using the water in the container?

Explanation of answer:

Step 1: This question requires us to first work out the volume of water in the container and then how many 2 litre bottles can be filled with that volume.

Step 2: We are given the length and width of the container, but remember that the depth of the water is 10 cm less that the height of the container. So the depth of the water is 40 cm – 10 cm = 30 cm.

Step 3: To find the volume of the water in the container we must multiply 60 cm x 50 cm x 30 cm. To simplify this calculation we can break it up as follows:

60 x 50 x 30 = 6 x 5 x 3 x 10 x 10 x 10

= 30 x 3 x 1000

= 90 x 1000

= 90,000.

So the volume of water is 90,000 cm³

Step 4: One cubic centimetre (1 cm³) is the same as one millilitre (1 ml). There are 1000 millilitres in a litre, so to find out how many litres are in the container we need to divide 90,000 by 1,000.

90,000 cm³ ÷ 1,000 = 90,000 ml

= 90,000 ml ÷ 1,000

= 90 litres.

There are 90 litres of water in the container.

Step 5: Now we need to divide the 90 litres by 2 as we are trying to fill 2-litre bottles.

90 ÷ 2 = 45, so Grant would be able to fill 45, 2-litre bottles using the water in the container.

Step 5: The correct answer is – a) 45 bottles

a) 45 bottles Correct Answer

b) 43 bottles Refer to Explanation of Answer

c) 38 bottles Refer to Explanation of Answer

d) 35 bottles Refer to Explanation of Answer

None

Question 176.

Before slikpik, lotto players had to choose six numbers from 1 to 45.

To win the lotto jackpot, they had to have all six numbers corresponding to the lotto draw.

Charlotte’s numbers were:     16, 17, 25, 27, 36, 42

Matilda’s numbers were:        15, 20, 25, 30, 35, 45

Olivia’s numbers were:           9, 13, 21, 28, 41, 45

Which one of these statements is true?

Explanation of answer:

Step 1: Whenever reading a question on chance like this one, it is important to understand that in any chance event that requires a random selection of numbers, every person involved in that chance event has an equal chance of winning. Regardless of which numbers a person chose or how they chose them, each number has the same probability of being drawn in the lotto.

Step 2: So in this question all three players have the same chance of winning.

Step 3: The correct answer is – c) All three players have the same chance of winning.

a) Olivia’s numbers are completely random, so she is the most likely to win. Refer to Explanation of Answer

b) Charlotte’s numbers are large, and hence have the best chance of winning. Refer to Explanation of Answer

c) All three players have the same chance of winning. Correct Answer

d) Matilda’s numbers have a pattern, so she has the least chance of winning. Refer to Explanation of Answer

None

Question 177.

A map of Perth Airport’s runway network has a scale of 1 : 50,000

On the map, the length of the main runway is 7 centimetres.

What is the actual length of the main runway?

Explanation of answer:

Step 1: The way to figure out the length of the runway is to use the scale ratio mentioned in the first sentence. The scale ratio says that 1 cm on the map is equivalent to 50,000 cm on the ground.

Step 2: We need to multiply the length of the runway on the map (7 cm) by the scale ratio of 50,000. We can remove the three zeros to make the multiplication easier. 7 x 50 = 350. Bring back the three zeros to the total to make 350,000. This means the runway is actually 350,000 cm long.

Step 3: There are 100 centimetres in a metre, so to convert 350,000 cm into metres we need to divide it by 100. This is simply done by dropping two zeros: 350,000 ÷ 100 = 3,500. So according to the map, the runway at Perth Airport is actually 3,500 metres long.

Step 4: The correct answer is – b) 3,500 m.

a) 4,000 metres Refer to Explanation of Answer

b) 3,500 metres Correct Answer

c) 3,250 metres Refer to Explanation of Answer

d) 3,000 metres Refer to Explanation of Answer

None

Question 178.

Tom found an old soup recipe that required him to use 4 pints of chicken stock and 2 pints of water in the soup.

A pint measures 568 millilitres in volume.

If Tom doesn’t add any other ingredients, what is the closest amount of soup that the recipe makes in litres?

Explanation of answer:

Step 1: This question is basically asking us covert millilitres to litres. We have 4 pints of chicken stock and 2 pints of water, giving us a total of 6 pints of fluid in the soup. We now need to multiply the 6 pints by the volume of the pint (568 mL). The question asks what is closest amount of soup made from the recipe. This says that we should have an approximate value from our calculations.

Step 2: To make the calculation easier we can round the volume of a pint from 568 mL up to 570 mL. Note that since we are only working with 6 pints, this rounding up will only increase our answer by 6 x 2 mL = 12 mL, which is the same as 0.012 litres – a very small inaccuracy.

Step 3: We need to multiply the 570 by 6. Break apart the 570 into two parts. 500 and 70. 500 mL x 6 = 3,000 mL and 70 mL x 6 = 420 mL. Add the two totals together 3,000 mL + 420 mL = 3,420 mL.

Step 3: Divide by 1,000 to convert the 3,420 mL to litres. 3,420 mL ÷ 1,000 = 3.42 litres. This becomes 3.4 litres if we round to one decimal place.

Step 4: The correct answer is – c) 3.4 litres

a) 3.8 litres Refer to Explanation of Answer

b) 3.5 litres Refer to Explanation of Answer

c) 3.4 litres Correct Answer

d) 3.1 litres Refer to Explanation of Answer

None

Question 179.

The middle triangle that is formed in this roof truss is an isosceles triangle.

What is the size of the angle labelled x?

Explanation of answer:

Step 1: The first piece of information that we need to know, is the characteristics of an isosceles triangle. An isosceles triangle has two sides and two angles that are the same. In this instance the two sides that would be same are the sides coming from the apex of the roof. That means the two angles that are the same, are the bottom two angles.

Step 2: To find the value of x we also need to know that the interior angles of a triangle add up to 180°. This requires us to subtract the total value of the bottom two angles from 180° to give the value of x.

Step 3: If the bottom two angles are the same, we can calculate the total size of the two angles at the bottom of the triangle. This would be 72° x 2 = 144°.

Step 4: All that is required now is to subtract 144° from 180° to find the value of x. 180° – 144° = 36°.

Step 5: The correct answer is – b) 36°.

a) 23° Refer to Explanation of Answer

b) 36° Correct Answer

c) 42° Refer to Explanation of Answer

d) 48° Refer to Explanation of Answer

None

Question 180.

On a real estate website, the median sales price for a house in the suburb of Hill Valley was \$450,000.

During the last month 37 houses were sold, including one for \$1.5 million.

If the $1.5 million house is not included in the calculation of the median price, which statement would be true?

Explanation of answer:

Step 1: In statistical analysis the median is known as the “middle” number in a numerically ordered data set. Removing a number from the data set could change the median value because the number in the middle of the old set is no longer in the middle of the new set. However, the median number could also stay the same if there are multiple numbers in the remaining set that are the same as the original median number.

Step 2: If we take out the sale of the $1.5 million house from the data range, we could find that the median house price decreases because we have removed a number that was higher than the original median i.e. the original median is now positioned just above the new median. Note that if we take one number away from a set of 37 numbers, then we are left with 36 numbers. Since 36 is even, there is no middle number. In this case the mean is calculated as being the average of the two middle numbers in the set. So the new median could be lower, but it cannot be higher.

Step 3: As we don’t know the data set, we don’t know if it contains several numbers that are the same as the original median price. This means the new median price could remain the same.

Step 4: This gives us our answer that the median price must either stay the same or be lower.

Step 5: The correct answer is – a) The median price must either stay the same or be lower.

a) The median price must either stay the same or be lower. Correct Answer

b) The median price must either stay the same or be higher. Refer to Explanation of Answer

c) The median price must stay the same. Refer to Explanation of Answer

d) The median price must be lower. Refer to Explanation of Answer

None

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Numeracy (Questions 171-180)

Welcome to the OLNA Support Numeracy Skill Builder

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