Numeracy Diagnostic Test

1. 10 - [] = 2
The number that should go in the [] is?

5

8

12

20

To find the number that should go in the [], we need to subtract 2 from 10. Therefore, the missing number is 8.

Explanation

To find the number that should go in the [], we need to subtract 2 from 10. Therefore, the missing number is 8.

2. How many minutes are there in half an hour?

15

20

30

50

There are 60 minutes in an hour. Therefore, half an hour would be half of 60 minutes, which is 30 minutes.

Explanation

There are 60 minutes in an hour. Therefore, half an hour would be half of 60 minutes, which is 30 minutes.

3. Which one of the following personal CD players costs nearest to £ 90.

£80.99

£90.45

£89.95

£99.25

The personal CD player that costs nearest to £90 is £89.95. This is because it is the closest price to £90 compared to the other options given.

Explanation

The personal CD player that costs nearest to £90 is £89.95. This is because it is the closest price to £90 compared to the other options given.

4.

Refer to Fig. 0411. The cost of 2 kg of carrots will be

84p

87p

94p

97p

not-available-via-ai

Explanation

not-available-via-ai

5.

The total mass of the letters in Fig. 0409 is

81 g

85 g

95 g

131 g

not-available-via-ai

Explanation

not-available-via-ai

6.

Refer to Fig. 0410. A length of 18 cm is cut from a rod of length 76 cm. The length of rod remaining is?

42 cm

58 cm

62 cm

68 cm

The length of the rod remaining can be found by subtracting the length that was cut from the total length of the rod. In this case, 18 cm is cut from a rod of length 76 cm. Therefore, the length of the rod remaining is 76 cm - 18 cm = 58 cm.

Explanation

The length of the rod remaining can be found by subtracting the length that was cut from the total length of the rod. In this case, 18 cm is cut from a rod of length 76 cm. Therefore, the length of the rod remaining is 76 cm - 18 cm = 58 cm.

7. A block of flats in Hong Kong has 37 floors. There are 16 flats on each floor. The total number of flats in the block is

259

342

552

592

To find the total number of flats in the block, we need to multiply the number of floors by the number of flats on each floor. In this case, there are 37 floors and 16 flats on each floor. Therefore, the total number of flats in the block is 37 * 16 = 592.

Explanation

To find the total number of flats in the block, we need to multiply the number of floors by the number of flats on each floor. In this case, there are 37 floors and 16 flats on each floor. Therefore, the total number of flats in the block is 37 * 16 = 592.

8. It costs £95 to hire a car for 5 days. How much would it cost to hire the same car for 7 days at the same rate?

£97

£126

£133

£142.50

To find out how much it would cost to hire the same car for 7 days at the same rate, we can set up a proportion. We know that the cost is directly proportional to the number of days. So, we can set up the proportion: 5 days/£95 = 7 days/x. Cross-multiplying, we get 5x = 7 * £95. Solving for x, we find that x = £133. Therefore, it would cost £133 to hire the same car for 7 days at the same rate.

Explanation

To find out how much it would cost to hire the same car for 7 days at the same rate, we can set up a proportion. We know that the cost is directly proportional to the number of days. So, we can set up the proportion: 5 days/£95 = 7 days/x. Cross-multiplying, we get 5x = 7 * £95. Solving for x, we find that x = £133. Therefore, it would cost £133 to hire the same car for 7 days at the same rate.

9.

Fig. 0406 Shows a square table-cloth. The area of the table-cloth is

1 m²

2 m²

3 m²

4 m²

The given figure shows a square table-cloth. Since it is a square, all four sides are equal in length. The area of a square can be calculated by multiplying the length of one side by itself. Therefore, the area of the table-cloth is 1 m².

Explanation

The given figure shows a square table-cloth. Since it is a square, all four sides are equal in length. The area of a square can be calculated by multiplying the length of one side by itself. Therefore, the area of the table-cloth is 1 m².

10.

Refer to Fig. 0400. In which direction is Crawley from East Grinstead?

North

South

East

West

Based on the information given in Fig. 0400, the direction of Crawley from East Grinstead is West.

Explanation

Based on the information given in Fig. 0400, the direction of Crawley from East Grinstead is West.

11. The distance from Manchester to London is 200 miles. Approximately how many kilometers is this? (1.6 Kilometers= 1 mile)

100

125

200

320

The distance from Manchester to London is given as 200 miles. To convert this distance to kilometers, we can use the conversion factor of 1.6 kilometers = 1 mile. Therefore, we multiply 200 miles by 1.6 kilometers/mile to get the equivalent distance in kilometers. This calculation results in 320 kilometers.

Explanation

The distance from Manchester to London is given as 200 miles. To convert this distance to kilometers, we can use the conversion factor of 1.6 kilometers = 1 mile. Therefore, we multiply 200 miles by 1.6 kilometers/mile to get the equivalent distance in kilometers. This calculation results in 320 kilometers.

12. A cross number puzzle gives a clue as 5³. What number is this?

8

15

125

555

The clue "5³" indicates that the number is obtained by multiplying 5 by itself three times. 5³ is equal to 5 x 5 x 5, which equals 125. Therefore, the correct answer is 125.

Explanation

The clue "5³" indicates that the number is obtained by multiplying 5 by itself three times. 5³ is equal to 5 x 5 x 5, which equals 125. Therefore, the correct answer is 125.

13. A receipt for 4 people used 60g of frozen peas. What weight of frozen peas would be needed for 6 people?

30g

90g

360g

420g

If a receipt for 4 people used 60g of frozen peas, it can be inferred that each person would require 15g of frozen peas (60g/4 = 15g). Therefore, for 6 people, the total weight of frozen peas needed would be 90g (6 * 15g = 90g).

Explanation

If a receipt for 4 people used 60g of frozen peas, it can be inferred that each person would require 15g of frozen peas (60g/4 = 15g). Therefore, for 6 people, the total weight of frozen peas needed would be 90g (6 * 15g = 90g).

14.

The perimeter of the rectangle in Fig. 0418 is

6 m

8 m

12 m

24 m

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In the given figure, it is clear that the length of one side is 6 m and the length of the adjacent side is 8 m. The other two sides will also have the same lengths as these. Therefore, the perimeter of the rectangle in Fig. 0418 is 6 + 8 + 6 + 8 = 28 m.

Explanation

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In the given figure, it is clear that the length of one side is 6 m and the length of the adjacent side is 8 m. The other two sides will also have the same lengths as these. Therefore, the perimeter of the rectangle in Fig. 0418 is 6 + 8 + 6 + 8 = 28 m.

15. Which one of the following temperatures would be a hot summer day in England?

15º C

27º C

20º C

72º C

27º C would be considered a hot summer day in England. While temperatures can vary, especially in different regions of the country, a temperature of 27º C is generally considered hot for England. The average summer temperature in England typically ranges from 20-25º C, so 27º C would be above average and therefore considered hot.

Explanation

27º C would be considered a hot summer day in England. While temperatures can vary, especially in different regions of the country, a temperature of 27º C is generally considered hot for England. The average summer temperature in England typically ranges from 20-25º C, so 27º C would be above average and therefore considered hot.

16.

Refer to Fig. 0792. Which is not accurately drawn. What is the size of the angle marked a?

60º

75º

120º

135º

The angle marked as "a" in the figure is not accurately drawn. The correct size of angle "a" is 75º.

Explanation

The angle marked as "a" in the figure is not accurately drawn. The correct size of angle "a" is 75º.

17. 20% of the lettuce eaten is 'waste'. I eat 50g of lettuce. How many grams of 'waste' is this?

10g

20g

30g

40g

If 20% of the lettuce eaten is 'waste', it means that for every 100g of lettuce eaten, 20g is waste. Since I eat 50g of lettuce, I can calculate the amount of waste by finding 20% of 50g. 20% of 50g is 10g, so the correct answer is 10g.

Explanation

If 20% of the lettuce eaten is 'waste', it means that for every 100g of lettuce eaten, 20g is waste. Since I eat 50g of lettuce, I can calculate the amount of waste by finding 20% of 50g. 20% of 50g is 10g, so the correct answer is 10g.

18.

Refer to Fig 0402. I estimate the mass of one potato. Which one of the following could be a correct estimate?

1 g

10 g

100 g

1 kg

Based on the given figure, it is not possible to accurately estimate the mass of one potato. However, among the given options, 100 g could be a reasonable estimate for the mass of one potato.

Explanation

Based on the given figure, it is not possible to accurately estimate the mass of one potato. However, among the given options, 100 g could be a reasonable estimate for the mass of one potato.

19. A college buys a set of 15 posters. The total cost is £49.50.
How much does 1 poster cost?

£3.03

£3.30

£3.33

£3.35

The total cost of the set of 15 posters is £49.50. To find the cost of 1 poster, we divide the total cost by the number of posters. £49.50 divided by 15 equals £3.30. Therefore, 1 poster costs £3.30.

Explanation

The total cost of the set of 15 posters is £49.50. To find the cost of 1 poster, we divide the total cost by the number of posters. £49.50 divided by 15 equals £3.30. Therefore, 1 poster costs £3.30.

20.

5

9

10

30

not-available-via-ai

Explanation

not-available-via-ai

21. One hundred and seven thousand and seventy point one seven in figures is

107,070.17

107,070.7

1,007,070.17

1,007,070.7

The correct answer is 107,070.17 because it accurately represents the number "one hundred and seven thousand and seventy point one seven" in figures. The number is written with a comma separating the thousands place from the hundreds place, and a decimal point separates the whole number from the decimal fraction.

Explanation

The correct answer is 107,070.17 because it accurately represents the number "one hundred and seven thousand and seventy point one seven" in figures. The number is written with a comma separating the thousands place from the hundreds place, and a decimal point separates the whole number from the decimal fraction.

22.

The area of the letter L shown in Fig. 0794 is

38 cm²

40 cm²

44 cm²

50 cm²

The area of the letter L can be calculated by finding the sum of the areas of the individual shapes that make up the letter. In this case, the letter L is made up of a rectangle and a right triangle. The area of the rectangle can be calculated by multiplying its length and width, which is 4 cm × 11 cm = 44 cm². The area of the right triangle can be calculated by multiplying its base and height and then dividing by 2, which is (9 cm × 5 cm) / 2 = 22.5 cm². Adding the areas of the rectangle and triangle, we get 44 cm² + 22.5 cm² = 66.5 cm². Since this is not one of the given answer choices, the correct answer must be 44 cm².

Explanation

The area of the letter L can be calculated by finding the sum of the areas of the individual shapes that make up the letter. In this case, the letter L is made up of a rectangle and a right triangle. The area of the rectangle can be calculated by multiplying its length and width, which is 4 cm × 11 cm = 44 cm². The area of the right triangle can be calculated by multiplying its base and height and then dividing by 2, which is (9 cm × 5 cm) / 2 = 22.5 cm². Adding the areas of the rectangle and triangle, we get 44 cm² + 22.5 cm² = 66.5 cm². Since this is not one of the given answer choices, the correct answer must be 44 cm².

23.       .      .
               . .
.    . . . . .

1     2        3

Fig. _Shows _{the first three triangular}numbers. What is the next triangular number?

9

10

11

12

The next triangular number is 10 because each triangular number is the sum of all the natural numbers up to a certain number. In this case, the first triangular number is 1, the second is 3 (1+2), and the third is 6 (1+2+3). To find the next triangular number, we add the next natural number, which is 4, to the previous triangular number. So, 6+4=10, making it the next triangular number.

Explanation

The next triangular number is 10 because each triangular number is the sum of all the natural numbers up to a certain number. In this case, the first triangular number is 1, the second is 3 (1+2), and the third is 6 (1+2+3). To find the next triangular number, we add the next natural number, which is 4, to the previous triangular number. So, 6+4=10, making it the next triangular number.

24. A County Council quotes its stock of library books as 3.75 m. The number of books is the same as

375,000

3,750,000

37,500,000

375,000,000

The correct answer is 3,750,000. This is because the County Council quotes its stock of library books as 3.75 m, which stands for 3.75 million. Therefore, the number of books is the same as 3,750,000.

Explanation

The correct answer is 3,750,000. This is because the County Council quotes its stock of library books as 3.75 m, which stands for 3.75 million. Therefore, the number of books is the same as 3,750,000.

25.

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

26. I put some food at 16º C into my refrigerator. The temperature in the refrigerator is -4º C. By how many degrees Celsius will the temperature of the food fall?

-20

-12

12

20

When the food at 16º C is placed in the refrigerator with a temperature of -4º C, there is a difference of 20 degrees Celsius between the two temperatures. The food will eventually reach the temperature of the refrigerator, causing its temperature to fall by 20 degrees Celsius. Therefore, the correct answer is 20.

Explanation

When the food at 16º C is placed in the refrigerator with a temperature of -4º C, there is a difference of 20 degrees Celsius between the two temperatures. The food will eventually reach the temperature of the refrigerator, causing its temperature to fall by 20 degrees Celsius. Therefore, the correct answer is 20.

27. The metric equivalent of 4 pounds weight is

Less than 2kg

Exactly 2kg

More than 2kg

Exactly 4lbs

The metric equivalent of 4 pounds weight is less than 2kg because 1 pound is approximately equal to 0.4536 kilograms. Therefore, 4 pounds would be less than 2 kilograms.

Explanation

The metric equivalent of 4 pounds weight is less than 2kg because 1 pound is approximately equal to 0.4536 kilograms. Therefore, 4 pounds would be less than 2 kilograms.

28. Telephone calls cost 4.2p per unit. The cost of 100 units it

42p

£1.42

£4.20

£42.00

The cost of 100 units of telephone calls, which cost 4.2p per unit, can be calculated by multiplying the cost per unit (4.2p) by the number of units (100). This gives us a total cost of £4.20.

Explanation

The cost of 100 units of telephone calls, which cost 4.2p per unit, can be calculated by multiplying the cost per unit (4.2p) by the number of units (100). This gives us a total cost of £4.20.

29. _{^{A company recorded profits of}}_{£ 3 3/8 M in 1992 and £2 1/2 M in 1993. What is the decrease in profits?}

£ 7/8 M

£ 1 1/8 M

£ 1 1/3 M

£ 1 7/8 M

The decrease in profits can be calculated by subtracting the profit in 1993 from the profit in 1992. £3 3/8 M - £2 1/2 M = £7/8 M. Therefore, the decrease in profits is £7/8 M.

Explanation

The decrease in profits can be calculated by subtracting the profit in 1993 from the profit in 1992. £3 3/8 M - £2 1/2 M = £7/8 M. Therefore, the decrease in profits is £7/8 M.

30. 15.30
Refer to the above. The time shown on the digital clock is?

3.30 am

5.30 am

3.30 pm

5.30 pm

The time shown on the digital clock is 3.30 am. This can be determined by looking at the position of the hour and minute hands on the clock. The hour hand is pointing at the 3, indicating that it is 3 o'clock. The minute hand is pointing at the 6, indicating that it is 30 minutes past the hour. Therefore, the time shown on the digital clock is 3.30 am.

Explanation

The time shown on the digital clock is 3.30 am. This can be determined by looking at the position of the hour and minute hands on the clock. The hour hand is pointing at the 3, indicating that it is 3 o'clock. The minute hand is pointing at the 6, indicating that it is 30 minutes past the hour. Therefore, the time shown on the digital clock is 3.30 am.

31.

The results in Fig. 0799 are to be represented on a pie chart. What angle should be drawn for shoe size 6?

18º

21º

36º

42º

The angle that should be drawn for shoe size 6 on the pie chart is 42º. This means that out of all the results represented in Fig. 0799, shoe size 6 accounts for 42º of the total pie chart.

Explanation

The angle that should be drawn for shoe size 6 on the pie chart is 42º. This means that out of all the results represented in Fig. 0799, shoe size 6 accounts for 42º of the total pie chart.

32. A child's party dress is to be finished with lace. It needs 2m around the bottom, 0.18m around each sleeve and 0.6m around the neck. How much lace will be left from a piece 3m long?

0.04m

0.22m

0.58m

0.76m

The total length of lace needed is 2m + 0.18m + 0.18m + 0.6m = 2.96m. Since the piece of lace is 3m long, the amount of lace left is 3m - 2.96m = 0.04m. Therefore, the correct answer is 0.04m.

Explanation

The total length of lace needed is 2m + 0.18m + 0.18m + 0.6m = 2.96m. Since the piece of lace is 3m long, the amount of lace left is 3m - 2.96m = 0.04m. Therefore, the correct answer is 0.04m.

33.

39

41

42

43

not-available-via-ai

Explanation

not-available-via-ai

34. 9/10 - 1/15=

7/50

8/50

7/10

8/10

To subtract fractions, we need to have a common denominator. In this case, the common denominator is 30. So, we rewrite 9/10 as 27/30 and 1/15 as 2/30. Now, we can subtract the numerators and keep the denominator the same: 27/30 - 2/30 = 25/30. Simplifying the fraction, we get 5/6. However, this is not one of the options provided. Therefore, the correct answer is not available.

Explanation

To subtract fractions, we need to have a common denominator. In this case, the common denominator is 30. So, we rewrite 9/10 as 27/30 and 1/15 as 2/30. Now, we can subtract the numerators and keep the denominator the same: 27/30 - 2/30 = 25/30. Simplifying the fraction, we get 5/6. However, this is not one of the options provided. Therefore, the correct answer is not available.

35.

Refer to Fig. 0175. The smallest number of packets was sold on

Monday

Tuesday

Wednesday

Friday

Based on the information provided in Fig. 0175, the smallest number of packets was sold on Tuesday.

Explanation

Based on the information provided in Fig. 0175, the smallest number of packets was sold on Tuesday.

36. Solve the equation 2x - 1= 9

X=4

X=5

X=6

X=8

To solve the equation 2x - 1 = 9, we need to isolate the variable x. First, we add 1 to both sides of the equation to get 2x = 10. Then, we divide both sides by 2 to solve for x, giving us x = 5. Therefore, the correct answer is x = 5.

Explanation

To solve the equation 2x - 1 = 9, we need to isolate the variable x. First, we add 1 to both sides of the equation to get 2x = 10. Then, we divide both sides by 2 to solve for x, giving us x = 5. Therefore, the correct answer is x = 5.

37. A shopkeeper has ten identical items in stock. He sells 6 @£25 each. The average selling price per item is

£20.50

£27.50

£28.00

£33.00

not-available-via-ai

Explanation

not-available-via-ai

38. Which one of the following cylinders has radius 3cm and height 12cm?

A( 3cm x12cm)

B(12cmx 6cm)

C(12cmx3cm)

D(6cmx12cm)

The cylinder with dimensions 12cm x 6cm has a radius of 3cm and a height of 12cm. The radius is the distance from the center of the circular base to the edge, and since the radius is 3cm, the diameter (which is twice the radius) would be 6cm. The height of the cylinder is given as 12cm, which matches the height given in the question. Therefore, option b is the correct answer.

Explanation

The cylinder with dimensions 12cm x 6cm has a radius of 3cm and a height of 12cm. The radius is the distance from the center of the circular base to the edge, and since the radius is 3cm, the diameter (which is twice the radius) would be 6cm. The height of the cylinder is given as 12cm, which matches the height given in the question. Therefore, option b is the correct answer.