Learn by Novus · Open practice pack v1

Numerical reasoning: full practice bank: open practice pack

100 untimed questions across 10 authored sections.

This is untimed educational practice for one cognitive skill. It is not a clinical, diagnostic, employment, or professionally recognized assessment, and it does not produce an IQ score or credential.

Learner worksheet

One hundred short problems in ten themed sections, starting gently and building up. Work at your own pace from the numbers given in each question. No outside data or calculator tricks needed.

Choose one answer for each item. For a delayed-recall item, read its study text, cover it, and then answer without looking back.

Everyday arithmetic

Warm up with whole-number addition, subtraction, multiplication, and division.

1. numerical-reasoning-s01-q01

One shelf holds 24 books and a second shelf holds 38 books. How many books are there altogether?

  1. 62
  2. 64
  3. 68
  4. 72

Answer:

2. numerical-reasoning-s01-q02

A box of 96 pencils is shared equally among 8 pupils. How many pencils does each pupil receive?

  1. 6
  2. 8
  3. 10
  4. 12

Answer:

3. numerical-reasoning-s01-q03

Cinema tickets cost £9 each. What is the total cost of 7 tickets?

  1. £56
  2. £63
  3. £66
  4. £72

Answer:

4. numerical-reasoning-s01-q04

A tank holds 500 litres of water. If 137 litres are drained out, how many litres remain?

  1. 337 litres
  2. 353 litres
  3. 363 litres
  4. 373 litres

Answer:

5. numerical-reasoning-s01-q05

What is the value of 18 − 12 ÷ 3?

  1. 2
  2. 6
  3. 10
  4. 14

Answer:

6. numerical-reasoning-s01-q06

A train has 6 carriages and each carriage seats 72 passengers. How many seats does the train have in total?

  1. 432
  2. 440
  3. 452
  4. 468

Answer:

7. numerical-reasoning-s01-q07

A crate contains 12 boxes, and each box holds 15 apples. How many apples are in the crate?

  1. 175
  2. 180
  3. 185
  4. 190

Answer:

8. numerical-reasoning-s01-q08

75 chairs are arranged into complete rows of 9, with any spare chairs left at the side. How many chairs are left over?

  1. 0
  2. 1
  3. 2
  4. 3

Answer:

9. numerical-reasoning-s01-q09

What is the value of 7 × 8 − 6?

  1. 50
  2. 52
  3. 56
  4. 62

Answer:

10. numerical-reasoning-s01-q10

A shop opens at 9:00 am and closes at 5:30 pm. For how many hours is it open?

  1. 7.5 hours
  2. 8 hours
  3. 8.5 hours
  4. 9 hours

Answer:

Fractions and decimals

Add, compare, and convert simple fractions and decimals.

11. numerical-reasoning-s02-q01

What is 1/2 + 1/4?

  1. 2/6
  2. 3/4
  3. 5/6
  4. 1 1/4

Answer:

12. numerical-reasoning-s02-q02

What is 3/5 of 40?

  1. 24
  2. 26
  3. 28
  4. 32

Answer:

13. numerical-reasoning-s02-q03

What is 0.25 × 80?

  1. 8
  2. 12
  3. 16
  4. 20

Answer:

14. numerical-reasoning-s02-q04

Which of these fractions is the largest?

  1. 3/5
  2. 7/12
  3. 2/3
  4. 5/8

Answer:

15. numerical-reasoning-s02-q05

What is 7.2 − 3.85?

  1. 3.35
  2. 3.45
  3. 3.55
  4. 4.35

Answer:

16. numerical-reasoning-s02-q06

A ribbon 3.6 metres long is cut into pieces each 0.4 metres long. How many pieces are made?

  1. 8
  2. 9
  3. 10
  4. 12

Answer:

17. numerical-reasoning-s02-q07

What is 18/24 written in its simplest form?

  1. 2/3
  2. 4/6
  3. 6/8
  4. 3/4

Answer:

18. numerical-reasoning-s02-q08

Two thirds of a class of 27 pupils walk to school. How many pupils walk?

  1. 12
  2. 18
  3. 21
  4. 24

Answer:

19. numerical-reasoning-s02-q09

What is 0.3 × 0.4?

  1. 0.12
  2. 0.7
  3. 1.2
  4. 12

Answer:

20. numerical-reasoning-s02-q10

A recipe needs 3/4 of a cup of flour. If you triple the recipe, how many cups of flour do you need?

  1. 1 1/2
  2. 2
  3. 2 1/4
  4. 2 3/4

Answer:

Percentages

Find percentages of amounts, and express changes as percentages.

21. numerical-reasoning-q1

A jacket normally costs $80. It is discounted by 25%. What is the sale price?

  1. $55
  2. $60
  3. $65
  4. $70

Answer:

22. numerical-reasoning-s03-q02

What is 15% of 60?

  1. 3
  2. 6
  3. 7.5
  4. 9

Answer:

23. numerical-reasoning-s03-q03

A pupil scores 45 marks out of 60. What percentage is this?

  1. 75%
  2. 80%
  3. 85%
  4. 90%

Answer:

24. numerical-reasoning-s03-q04

A price rises from £50 to £58. What is the percentage increase?

  1. 8%
  2. 16%
  3. 18%
  4. 20%

Answer:

25. numerical-reasoning-s03-q05

A restaurant meal costs £40, and a 12.5% service charge is added. What is the total bill?

  1. £42
  2. £44
  3. £45
  4. £47.50

Answer:

26. numerical-reasoning-q3

In a class of 30 students, 40% are boys. How many girls are in the class?

  1. 12
  2. 15
  3. 18
  4. 20

Answer:

27. numerical-reasoning-s03-q07

30% of a number is 21. What is the number?

  1. 70
  2. 72
  3. 75
  4. 90

Answer:

28. numerical-reasoning-s03-q08

A test is marked out of 25. A pupil scores 68%. How many marks did they get?

  1. 14
  2. 15
  3. 16
  4. 17

Answer:

29. numerical-reasoning-s03-q09

A village's population falls from 2,500 to 2,300 over a decade. What is the percentage decrease?

  1. 6%
  2. 8%
  3. 9%
  4. 10%

Answer:

30. numerical-reasoning-s03-q10

Which is greater: 25% of 80, or 30% of 70?

  1. 30% of 70
  2. 25% of 80
  3. They are equal
  4. It cannot be determined

Answer:

Ratios and proportion

Share amounts in a given ratio and scale quantities proportionally.

31. numerical-reasoning-s04-q01

£60 is shared between two people in the ratio 2 : 1. How much does the person with the larger share receive?

  1. £30
  2. £40
  3. £45
  4. £50

Answer:

32. numerical-reasoning-s04-q02

A shelter houses 12 cats and 18 dogs. What is the ratio of cats to dogs in its simplest form?

  1. 3 : 2
  2. 6 : 9
  3. 2 : 3
  4. 4 : 6

Answer:

33. numerical-reasoning-s04-q03

A map uses a scale of 1 : 50,000. Two towns are 4 cm apart on the map. What is the real distance between them?

  1. 0.2 km
  2. 0.5 km
  3. 1 km
  4. 2 km

Answer:

34. numerical-reasoning-s04-q04

A squash drink is mixed from concentrate and water in the ratio 1 : 4. How much water is needed for 250 ml of concentrate?

  1. 1,000 ml
  2. 1,250 ml
  3. 1,500 ml
  4. 2,000 ml

Answer:

35. numerical-reasoning-q4

A recipe uses a ratio of 2 cups flour to 3 cups sugar. If you use 9 cups of sugar, how many cups of flour do you need?

  1. 4
  2. 5
  3. 6
  4. 7

Answer:

36. numerical-reasoning-s04-q06

45 sweets are shared between two children in the ratio 4 : 5. How many sweets does the child with the smaller share receive?

  1. 18
  2. 20
  3. 22
  4. 25

Answer:

37. numerical-reasoning-s04-q07

In a car park, the ratio of red cars to silver cars is 3 : 7. If there are 21 red cars, how many silver cars are there?

  1. 35
  2. 42
  3. 45
  4. 49

Answer:

38. numerical-reasoning-s04-q08

Three identical printers together produce 360 pages in an hour. At the same rate, how many pages would five such printers produce in an hour?

  1. 480
  2. 540
  3. 600
  4. 720

Answer:

39. numerical-reasoning-s04-q09

A biscuit mix uses flour, butter, and sugar in the ratio 3 : 2 : 1. If the mix weighs 480 g in total, how much butter does it contain?

  1. 80 g
  2. 160 g
  3. 240 g
  4. 320 g

Answer:

40. numerical-reasoning-s04-q10

8 identical pens cost £6. How much would 12 of the same pens cost?

  1. £9
  2. £10
  3. £10.50
  4. £12

Answer:

Rates, time, and conversions

Work with speed, unit rates, clock arithmetic, and unit conversions.

41. numerical-reasoning-q2

A car travels 180 km in 3 hours at a constant speed. How far will it travel in 5 hours at the same speed?

  1. 240 km
  2. 270 km
  3. 300 km
  4. 320 km

Answer:

42. numerical-reasoning-s05-q02

Convert 3,200 metres into kilometres.

  1. 3.2 km
  2. 32 km
  3. 320 km
  4. 3,200 km

Answer:

43. numerical-reasoning-s05-q03

A cyclist covers 45 km in 2.5 hours. What is her average speed?

  1. 12 km/h
  2. 15 km/h
  3. 16 km/h
  4. 18 km/h

Answer:

44. numerical-reasoning-s05-q04

A coach departs at 09:40 and the journey takes 1 hour 35 minutes. At what time does it arrive?

  1. 11:05
  2. 11:15
  3. 11:25
  4. 11:35

Answer:

45. numerical-reasoning-s05-q05

A tap fills a paddling pool at 4 litres per minute. How long will it take to fill a 90-litre pool?

  1. 20 minutes
  2. 21.5 minutes
  3. 22.5 minutes
  4. 24 minutes

Answer:

46. numerical-reasoning-s05-q06

Walking at a steady 5 km/h, how long does a 12 km walk take?

  1. 2 hours 24 minutes
  2. 2 hours 30 minutes
  3. 2 hours 36 minutes
  4. 2 hours 48 minutes

Answer:

47. numerical-reasoning-s05-q07

The exchange rate is £1 = €1.15. How many euros do you receive for £60?

  1. €63
  2. €65
  3. €66
  4. €69

Answer:

48. numerical-reasoning-s05-q08

Express 45 minutes as a decimal fraction of an hour.

  1. 0.45
  2. 0.6
  3. 0.75
  4. 0.8

Answer:

49. numerical-reasoning-s05-q09

A bottling machine fills 240 bottles in 20 minutes. At the same rate, how many bottles does it fill per hour?

  1. 480
  2. 720
  3. 960
  4. 1,200

Answer:

50. numerical-reasoning-s05-q10

A lorry travels at a steady 64 km/h for 2 hours 15 minutes. How far does it travel?

  1. 144 km
  2. 148 km
  3. 152 km
  4. 160 km

Answer:

Money and financial arithmetic

Handle change, wages, unit pricing, interest, and simple profit.

51. numerical-reasoning-s06-q01

You buy items costing £7.35 and £4.20, and pay with a £20 note. How much change should you receive?

  1. £8.35
  2. £8.45
  3. £8.55
  4. £9.45

Answer:

52. numerical-reasoning-s06-q02

A 500 g pack of rice costs £2.40 and a 750 g pack of the same rice costs £3.30. Which is the better value for money?

  1. The 750 g pack
  2. The 500 g pack
  3. Both offer identical value
  4. It cannot be determined

Answer:

53. numerical-reasoning-s06-q03

£800 is saved in an account paying 5% simple interest per year. How much interest is earned over 3 years?

  1. £40
  2. £80
  3. £100
  4. £120

Answer:

54. numerical-reasoning-s06-q04

A worker earns £2,400 per month and spends 35% of it on rent. How much is the rent?

  1. £760
  2. £800
  3. £840
  4. £960

Answer:

55. numerical-reasoning-q5

A $500 investment grows by 10% in year one, then by 10% of the new amount in year two. What is the value after two years?

  1. $590
  2. $600
  3. $605
  4. $610

Answer:

56. numerical-reasoning-s06-q06

A restaurant bill of £86.40 is split equally among 6 diners. How much does each pay?

  1. £13.40
  2. £14.40
  3. £14.60
  4. £15.40

Answer:

57. numerical-reasoning-s06-q07

A washing machine costs £640. A buyer pays a 15% deposit. How much is left to pay afterwards?

  1. £544
  2. £560
  3. £576
  4. £600

Answer:

58. numerical-reasoning-s06-q08

An employee works 38 hours in a week at £12.50 per hour. What is the weekly wage?

  1. £455
  2. £462.50
  3. £470
  4. £475

Answer:

59. numerical-reasoning-s06-q09

A shop runs a 'buy three, get one free' offer on drinks costing £2.50 each. How much do you pay if you take 8 drinks?

  1. £12.50
  2. £15
  3. £17.50
  4. £20

Answer:

60. numerical-reasoning-s06-q10

A trader buys 40 plants at £1.20 each and sells them all at £2 each. What is the total profit?

  1. £32
  2. £38
  3. £40
  4. £48

Answer:

Averages and simple data

Calculate and interpret means, medians, modes, ranges, and weighted averages.

61. numerical-reasoning-s07-q01

What is the mean of 4, 8, 9, and 11?

  1. 6
  2. 7
  3. 8
  4. 9

Answer:

62. numerical-reasoning-s07-q02

What is the median of 3, 7, 8, 12, and 15?

  1. 7
  2. 8
  3. 9
  4. 12

Answer:

63. numerical-reasoning-s07-q03

What is the mode of the data set 2, 4, 4, 5, 7, 4, 9?

  1. 4
  2. 5
  3. 7
  4. 9

Answer:

64. numerical-reasoning-s07-q04

What is the range of the data set 12, 5, 19, 8, 23?

  1. 11
  2. 15
  3. 18
  4. 23

Answer:

65. numerical-reasoning-s07-q05

The mean of five test scores is 14. Four of the scores are 12, 15, 10, and 18. What is the fifth score?

  1. 11
  2. 12
  3. 14
  4. 15

Answer:

66. numerical-reasoning-s07-q06

Class A has 20 pupils with a mean score of 60. Class B has 10 pupils with a mean score of 75. What is the mean score across both classes combined?

  1. 65
  2. 66
  3. 67.5
  4. 70

Answer:

67. numerical-reasoning-s07-q07

A van drives 120 km in the first 2 hours, then 60 km in the next hour. What is its average speed over the whole journey?

  1. 55 km/h
  2. 60 km/h
  3. 65 km/h
  4. 67.5 km/h

Answer:

68. numerical-reasoning-s07-q08

A stall's sales were 40 cakes on Monday, 55 on Tuesday, and 25 on Wednesday. What was the mean daily sale?

  1. 35
  2. 38
  3. 40
  4. 45

Answer:

69. numerical-reasoning-s07-q09

The mean of six numbers is 10. A seventh number, 24, is added to the set. What is the new mean?

  1. 10.5
  2. 11
  3. 11.5
  4. 12

Answer:

70. numerical-reasoning-s07-q10

A quiz team of five players has a mean score of 50 points per player. What is the highest score achieved by any single player?

  1. It cannot be determined from the information given
  2. Exactly 50
  3. Exactly 250
  4. At least 60

Answer:

Number sequences and relationships

Find the rule behind each sequence, then apply it to the missing term.

71. numerical-reasoning-s08-q01

What is the next number in the sequence 5, 9, 13, 17, ...?

  1. 18
  2. 19
  3. 20
  4. 21

Answer:

72. numerical-reasoning-s08-q02

What is the next number in the sequence 2, 6, 18, 54, ...?

  1. 108
  2. 148
  3. 162
  4. 216

Answer:

73. numerical-reasoning-s08-q03

What is the next number in the sequence 64, 32, 16, 8, ...?

  1. 2
  2. 4
  3. 5
  4. 6

Answer:

74. numerical-reasoning-s08-q04

What is the next number in the sequence 1, 4, 9, 16, 25, ...?

  1. 36
  2. 42
  3. 49
  4. 50

Answer:

75. numerical-reasoning-s08-q05

What is the next number in the sequence 3, 4, 7, 11, 18, ...?

  1. 29
  2. 30
  3. 32
  4. 36

Answer:

76. numerical-reasoning-s08-q06

What is the next number in the sequence 40, 37, 33, 28, 22, ...?

  1. 14
  2. 15
  3. 16
  4. 17

Answer:

77. numerical-reasoning-s08-q07

What is the next number in the sequence 1, 10, 3, 8, 5, 6, 7, ...?

  1. 4
  2. 5
  3. 6
  4. 8

Answer:

78. numerical-reasoning-s08-q08

What is the next number in the sequence 5, 6, 8, 11, 15, 20, ...?

  1. 24
  2. 25
  3. 26
  4. 27

Answer:

79. numerical-reasoning-s08-q09

Which number does not belong with the others: 8, 27, 64, 100, 125?

  1. 27
  2. 64
  3. 100
  4. 125

Answer:

80. numerical-reasoning-s08-q10

A sequence follows the rule 'double the previous term, then subtract 1': 3, 5, 9, 17, ... What is the next term?

  1. 31
  2. 33
  3. 34
  4. 35

Answer:

Multi-step word problems

Combine two or more operations: plan the steps before you calculate.

81. numerical-reasoning-s09-q01

A hall has 18 rows of 22 seats. If 315 tickets are sold for a concert, how many seats remain empty?

  1. 71
  2. 79
  3. 81
  4. 91

Answer:

82. numerical-reasoning-s09-q02

A plumber charges a £40 call-out fee plus £15 per hour of work. If a bill comes to £145, how many hours did the job take?

  1. 6
  2. 7
  3. 8
  4. 9

Answer:

83. numerical-reasoning-s09-q03

A car uses 6 litres of fuel per 100 km, and fuel costs £1.50 per litre. How much does the fuel for a 450 km trip cost?

  1. £36.00
  2. £37.50
  3. £40.00
  4. £40.50

Answer:

84. numerical-reasoning-s09-q04

A jumper priced at £45 is reduced by 20% in a sale, and a £5 voucher is then taken off the sale price. What do you pay?

  1. £31
  2. £32
  3. £35
  4. £36

Answer:

85. numerical-reasoning-s09-q05

Amir is twice as old as Beth, and their ages add up to 36. How old is Amir?

  1. 18
  2. 20
  3. 24
  4. 27

Answer:

86. numerical-reasoning-s09-q06

A number is multiplied by 4 and then 6 is added, giving 46. What was the original number?

  1. 7
  2. 8
  3. 9
  4. 10

Answer:

87. numerical-reasoning-s09-q07

A warehouse holds 1,200 units. On Monday it ships out 15% of its stock, and on Tuesday it receives a delivery of 250 units. How many units does it hold after Tuesday?

  1. 1,270
  2. 1,330
  3. 1,370
  4. 1,450

Answer:

88. numerical-reasoning-s09-q08

A floor measures 4 m by 3 m. Each tile covers 0.25 m², and tiles are sold in boxes of 10. How many boxes are needed to cover the floor exactly?

  1. 4
  2. 5
  3. 6
  4. 48

Answer:

89. numerical-reasoning-s09-q09

Adult tickets cost £9 and child tickets cost £5. A family buys 2 adult and 3 child tickets, paying with a £50 note. How much change do they receive?

  1. £14
  2. £15
  3. £16
  4. £17

Answer:

90. numerical-reasoning-s09-q10

A shop's June sales were 20% higher than its May sales. June sales were 660 units. How many units were sold in May?

  1. 550
  2. 572
  3. 605
  4. 792

Answer:

Compound change and combined rates

The toughest set: repeated percentage change, reverse percentages, and rates working together.

91. numerical-reasoning-s10-q01

A machine worth £2,000 loses 10% of its value each year. What is it worth after two years?

  1. £1,600
  2. £1,620
  3. £1,640
  4. £1,800

Answer:

92. numerical-reasoning-s10-q02

A coat priced at £150 is reduced by 20%, and the sale price is later reduced by a further 10%. What is the final price?

  1. £102
  2. £104
  3. £105
  4. £108

Answer:

93. numerical-reasoning-s10-q03

After a 20% price increase, a ticket costs £96. What did it cost before the increase?

  1. £80
  2. £84
  3. £88
  4. £92

Answer:

94. numerical-reasoning-s10-q04

Working alone, machine A completes a job in 3 hours. Working together, machines A and B complete the same job in 2 hours. How long would machine B take alone?

  1. 4 hours
  2. 5 hours
  3. 6 hours
  4. 12 hours

Answer:

95. numerical-reasoning-s10-q05

A driver travels from town P to town Q at 60 km/h and returns along the same road at 40 km/h. What is the average speed for the whole round trip?

  1. 45 km/h
  2. 48 km/h
  3. 50 km/h
  4. 52 km/h

Answer:

96. numerical-reasoning-s10-q06

In a company, 30% of the staff work part-time, and 40% of those part-time staff work at weekends. What percentage of all staff are part-time weekend workers?

  1. 8%
  2. 10%
  3. 11%
  4. 12%

Answer:

97. numerical-reasoning-s10-q07

Without calculating exactly, which is the best estimate of 41,872 ÷ 68.9?

  1. About 600
  2. About 6,000
  3. About 60,000
  4. About 600,000

Answer:

98. numerical-reasoning-q6

Pipe A fills a tank alone in 4 hours; pipe B fills it alone in 6 hours. Working together, about how many hours will it take?

  1. 2 hours
  2. 2.4 hours
  3. 3 hours
  4. 5 hours

Answer:

99. numerical-reasoning-s10-q09

A bag contains red and blue counters in the ratio 3 : 2, and holds 30 counters in total. If 6 more blue counters are added, what is the new ratio of red to blue?

  1. 3 : 2
  2. 6 : 5
  3. 1 : 1
  4. 2 : 3

Answer:

100. numerical-reasoning-s10-q10

An investment rises in value by 25% in its first year and then falls by 20% in its second year. What is the overall effect on its value?

  1. A 5% overall increase
  2. No overall change
  3. A 5% overall decrease
  4. A 10% overall increase

Answer:

Authored hints

This cognitive practice source does not publish authored hints. Every item is listed as missing a hint, and no hint text is generated or inferred.

100 worksheet items do not have an authored hint.

This source contains no authored hints. No hint text was generated.

Answer key

ItemChoiceAnswer
numerical-reasoning-s01-q01A62
numerical-reasoning-s01-q02D12
numerical-reasoning-s01-q03B£63
numerical-reasoning-s01-q04C363 litres
numerical-reasoning-s01-q05D14
numerical-reasoning-s01-q06A432
numerical-reasoning-s01-q07B180
numerical-reasoning-s01-q08D3
numerical-reasoning-s01-q09A50
numerical-reasoning-s01-q10C8.5 hours
numerical-reasoning-s02-q01B3/4
numerical-reasoning-s02-q02A24
numerical-reasoning-s02-q03D20
numerical-reasoning-s02-q04C2/3
numerical-reasoning-s02-q05A3.35
numerical-reasoning-s02-q06B9
numerical-reasoning-s02-q07D3/4
numerical-reasoning-s02-q08B18
numerical-reasoning-s02-q09A0.12
numerical-reasoning-s02-q10C2 1/4
numerical-reasoning-q1B$60
numerical-reasoning-s03-q02D9
numerical-reasoning-s03-q03A75%
numerical-reasoning-s03-q04B16%
numerical-reasoning-s03-q05C£45
numerical-reasoning-q3C18
numerical-reasoning-s03-q07A70
numerical-reasoning-s03-q08D17
numerical-reasoning-s03-q09B8%
numerical-reasoning-s03-q10A30% of 70
numerical-reasoning-s04-q01B£40
numerical-reasoning-s04-q02C2 : 3
numerical-reasoning-s04-q03D2 km
numerical-reasoning-s04-q04A1,000 ml
numerical-reasoning-q4C6
numerical-reasoning-s04-q06B20
numerical-reasoning-s04-q07D49
numerical-reasoning-s04-q08C600
numerical-reasoning-s04-q09B160 g
numerical-reasoning-s04-q10A£9
numerical-reasoning-q2C300 km
numerical-reasoning-s05-q02A3.2 km
numerical-reasoning-s05-q03D18 km/h
numerical-reasoning-s05-q04B11:15
numerical-reasoning-s05-q05C22.5 minutes
numerical-reasoning-s05-q06A2 hours 24 minutes
numerical-reasoning-s05-q07D€69
numerical-reasoning-s05-q08C0.75
numerical-reasoning-s05-q09B720
numerical-reasoning-s05-q10A144 km
numerical-reasoning-s06-q01B£8.45
numerical-reasoning-s06-q02AThe 750 g pack
numerical-reasoning-s06-q03D£120
numerical-reasoning-s06-q04C£840
numerical-reasoning-q5C$605
numerical-reasoning-s06-q06B£14.40
numerical-reasoning-s06-q07A£544
numerical-reasoning-s06-q08D£475
numerical-reasoning-s06-q09B£15
numerical-reasoning-s06-q10A£32
numerical-reasoning-s07-q01C8
numerical-reasoning-s07-q02B8
numerical-reasoning-s07-q03A4
numerical-reasoning-s07-q04C18
numerical-reasoning-s07-q05D15
numerical-reasoning-s07-q06A65
numerical-reasoning-s07-q07B60 km/h
numerical-reasoning-s07-q08C40
numerical-reasoning-s07-q09D12
numerical-reasoning-s07-q10AIt cannot be determined from the information given
numerical-reasoning-s08-q01D21
numerical-reasoning-s08-q02C162
numerical-reasoning-s08-q03B4
numerical-reasoning-s08-q04A36
numerical-reasoning-s08-q05A29
numerical-reasoning-s08-q06B15
numerical-reasoning-s08-q07A4
numerical-reasoning-s08-q08C26
numerical-reasoning-s08-q09C100
numerical-reasoning-s08-q10B33
numerical-reasoning-s09-q01C81
numerical-reasoning-s09-q02B7
numerical-reasoning-s09-q03D£40.50
numerical-reasoning-s09-q04A£31
numerical-reasoning-s09-q05C24
numerical-reasoning-s09-q06D10
numerical-reasoning-s09-q07A1,270
numerical-reasoning-s09-q08B5
numerical-reasoning-s09-q09D£17
numerical-reasoning-s09-q10A550
numerical-reasoning-s10-q01B£1,620
numerical-reasoning-s10-q02D£108
numerical-reasoning-s10-q03A£80
numerical-reasoning-s10-q04C6 hours
numerical-reasoning-s10-q05B48 km/h
numerical-reasoning-s10-q06D12%
numerical-reasoning-s10-q07AAbout 600
numerical-reasoning-q6B2.4 hours
numerical-reasoning-s10-q09C1 : 1
numerical-reasoning-s10-q10BNo overall change

Worked explanations

numerical-reasoning-s01-q01

Add the two shelf counts directly: 24 + 38 = 62.

numerical-reasoning-s01-q02

Equal sharing is division: 96 ÷ 8 = 12 pencils each.

numerical-reasoning-s01-q03

Repeated equal amounts call for multiplication: 7 × £9 = £63.

numerical-reasoning-s01-q04

Subtract the drained amount from the full tank: 500 − 137 = 363 litres.

numerical-reasoning-s01-q05

Division is carried out before subtraction: 12 ÷ 3 = 4, so 18 − 4 = 14. Working left to right first would wrongly give 2.

numerical-reasoning-s01-q06

Multiply carriages by seats per carriage: 6 × 72 = 432.

numerical-reasoning-s01-q07

Multiply the number of boxes by apples per box: 12 × 15 = 180.

numerical-reasoning-s01-q08

9 × 8 = 72 is the largest multiple of 9 that fits within 75, leaving a remainder of 75 − 72 = 3.

numerical-reasoning-s01-q09

Multiplication comes before subtraction: 7 × 8 = 56, then 56 − 6 = 50.

numerical-reasoning-s01-q10

From 9:00 am to 5:00 pm is 8 hours, plus the extra 30 minutes makes 8.5 hours.

numerical-reasoning-s02-q01

Convert to a common denominator first: 1/2 = 2/4, so 2/4 + 1/4 = 3/4. Adding tops and bottoms separately is the classic trap.

numerical-reasoning-s02-q02

Find one fifth first: 40 ÷ 5 = 8, then multiply by three: 3 × 8 = 24.

numerical-reasoning-s02-q03

0.25 is one quarter, so multiplying by it is dividing by 4: 80 ÷ 4 = 20.

numerical-reasoning-s02-q04

Converting to decimals makes the comparison easy: 3/5 = 0.6, 7/12 ≈ 0.583, 2/3 ≈ 0.667, and 5/8 = 0.625, so 2/3 is largest.

numerical-reasoning-s02-q05

Line up the decimal places by writing 7.2 as 7.20, then subtract: 7.20 − 3.85 = 3.35.

numerical-reasoning-s02-q06

Divide the total length by the piece length: 3.6 ÷ 0.4 = 36 ÷ 4 = 9 pieces.

numerical-reasoning-s02-q07

Divide top and bottom by their highest common factor, 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4. Equivalent fractions like 6/8 are not fully simplified.

numerical-reasoning-s02-q08

One third of 27 is 9, so two thirds is 2 × 9 = 18 pupils.

numerical-reasoning-s02-q09

Multiply as whole numbers (3 × 4 = 12), then place two decimal digits because the factors have one each: 0.12.

numerical-reasoning-s02-q10

Multiply the fraction by three: 3 × 3/4 = 9/4, which is 2 1/4 cups.

numerical-reasoning-q1

25% of $80 is $20, so the sale price is $80 − $20 = $60.

numerical-reasoning-s03-q02

10% of 60 is 6 and 5% is 3, so 15% is 6 + 3 = 9.

numerical-reasoning-s03-q03

Divide the score by the total and multiply by 100: 45 ÷ 60 = 0.75, which is 75%.

numerical-reasoning-s03-q04

Percentage change is the change divided by the original amount: 8 ÷ 50 = 0.16, so a 16% increase.

numerical-reasoning-s03-q05

12.5% is one eighth, so the charge is £40 ÷ 8 = £5, giving £40 + £5 = £45.

numerical-reasoning-q3

40% of 30 is 12 boys, so the remaining 30 − 12 = 18 students are girls.

numerical-reasoning-s03-q07

If 30% is 21, then 10% is 21 ÷ 3 = 7, so the whole number (100%) is 7 × 10 = 70.

numerical-reasoning-s03-q08

Convert the percentage to a decimal and multiply: 0.68 × 25 = 17 marks.

numerical-reasoning-s03-q09

The fall is 200 people; divide by the original population: 200 ÷ 2,500 = 0.08, an 8% decrease.

numerical-reasoning-s03-q10

Work both out: 25% of 80 is 20, while 30% of 70 is 21, so 30% of 70 is slightly greater.

numerical-reasoning-s04-q01

The ratio 2 : 1 has 3 equal parts, each worth £60 ÷ 3 = £20; the larger share is 2 × £20 = £40.

numerical-reasoning-s04-q02

Divide both sides by their highest common factor, 6: 12 : 18 becomes 2 : 3. Keep the order as asked: cats first.

numerical-reasoning-s04-q03

Multiply the map distance by the scale: 4 cm × 50,000 = 200,000 cm, and converting units gives 2,000 m = 2 km.

numerical-reasoning-s04-q04

Every 1 part of concentrate needs 4 parts of water, so 250 ml needs 4 × 250 = 1,000 ml of water.

numerical-reasoning-q4

9 cups of sugar is 3× the ratio's 3 cups, so flour scales the same way: 2 × 3 = 6 cups.

numerical-reasoning-s04-q06

The ratio 4 : 5 has 9 parts, each worth 45 ÷ 9 = 5 sweets; the smaller share is 4 × 5 = 20.

numerical-reasoning-s04-q07

21 red cars is 7 times the ratio's 3, so scale the silver side the same way: 7 × 7 = 49.

numerical-reasoning-s04-q08

Each printer produces 360 ÷ 3 = 120 pages per hour, so five produce 5 × 120 = 600.

numerical-reasoning-s04-q09

The ratio has 3 + 2 + 1 = 6 parts, each worth 480 ÷ 6 = 80 g; butter is 2 parts, so 160 g.

numerical-reasoning-s04-q10

One pen costs £6 ÷ 8 = £0.75, so 12 pens cost 12 × £0.75 = £9.

numerical-reasoning-q2

180 km ÷ 3 h = 60 km/h. At 60 km/h for 5 hours: 60 × 5 = 300 km.

numerical-reasoning-s05-q02

There are 1,000 metres in a kilometre, so divide by 1,000: 3,200 m = 3.2 km.

numerical-reasoning-s05-q03

Average speed is distance divided by time: 45 ÷ 2.5 = 18 km/h.

numerical-reasoning-s05-q04

Break the journey into easy steps: 09:40 plus 20 minutes reaches 10:00, and the remaining 1 hour 15 minutes reaches 11:15.

numerical-reasoning-s05-q05

Divide the volume by the rate: 90 ÷ 4 = 22.5 minutes.

numerical-reasoning-s05-q06

Time is distance divided by speed: 12 ÷ 5 = 2.4 hours, and 0.4 of an hour is 0.4 × 60 = 24 minutes.

numerical-reasoning-s05-q07

Multiply the pounds by the rate per pound: 60 × 1.15 = €69.

numerical-reasoning-s05-q08

Divide by the 60 minutes in an hour: 45 ÷ 60 = 0.75. Writing 45 minutes as 0.45 hours is the common slip.

numerical-reasoning-s05-q09

An hour contains three 20-minute periods, so the hourly total is 3 × 240 = 720 bottles.

numerical-reasoning-s05-q10

Convert the time to a decimal: 2 hours 15 minutes = 2.25 hours, then multiply: 64 × 2.25 = 144 km.

numerical-reasoning-s06-q01

The total spend is £7.35 + £4.20 = £11.55, so the change is £20 − £11.55 = £8.45.

numerical-reasoning-s06-q02

Compare a common unit: per 100 g, the small pack costs £2.40 ÷ 5 = £0.48 while the large pack costs £3.30 ÷ 7.5 = £0.44, so the larger pack is cheaper per gram.

numerical-reasoning-s06-q03

Simple interest pays the same amount each year: 5% of £800 is £40, so three years earn 3 × £40 = £120.

numerical-reasoning-s06-q04

10% of £2,400 is £240, so 35% is 3.5 × £240 = £840.

numerical-reasoning-q5

$500 × 1.10 = $550 after year one; $550 × 1.10 = $605 after year two.

numerical-reasoning-s06-q06

Divide the bill by the number of diners: £86.40 ÷ 6 = £14.40.

numerical-reasoning-s06-q07

The deposit is 15% of £640 = £96, leaving £640 − £96 = £544, or simply take 85% of the price directly.

numerical-reasoning-s06-q08

Multiply hours by the hourly rate: 38 × £12.50 = £475. Doubling £12.50 to £25 per 2 hours makes the mental sum easier: 19 × £25 = £475.

numerical-reasoning-s06-q09

Eight drinks form two groups of four, and in each group one is free, so you pay for 6 drinks: 6 × £2.50 = £15.

numerical-reasoning-s06-q10

The profit per plant is £2 − £1.20 = £0.80, so 40 plants earn 40 × £0.80 = £32.

numerical-reasoning-s07-q01

Add the values and divide by how many there are: (4 + 8 + 9 + 11) ÷ 4 = 32 ÷ 4 = 8.

numerical-reasoning-s07-q02

With the five values already in order, the median is the middle (third) value: 8.

numerical-reasoning-s07-q03

The mode is the most frequent value, and 4 appears three times, more than any other.

numerical-reasoning-s07-q04

The range is the largest value minus the smallest: 23 − 5 = 18.

numerical-reasoning-s07-q05

A mean of 14 across five scores means a total of 5 × 14 = 70; the four known scores sum to 55, so the fifth is 70 − 55 = 15.

numerical-reasoning-s07-q06

Weight each mean by its class size: total marks are 20 × 60 + 10 × 75 = 1,950, spread over 30 pupils gives 65. Simply averaging 60 and 75 ignores the different class sizes.

numerical-reasoning-s07-q07

Average speed is total distance over total time: (120 + 60) ÷ (2 + 1) = 180 ÷ 3 = 60 km/h.

numerical-reasoning-s07-q08

Sum the three days and divide by three: (40 + 55 + 25) ÷ 3 = 120 ÷ 3 = 40.

numerical-reasoning-s07-q09

The original total is 6 × 10 = 60; adding 24 gives 84 across seven numbers, and 84 ÷ 7 = 12.

numerical-reasoning-s07-q10

A mean only fixes the total (5 × 50 = 250 points), not how the points are spread. Every player could have scored exactly 50, or one could have scored far more.

numerical-reasoning-s08-q01

Each term increases by 4, so the next term is 17 + 4 = 21.

numerical-reasoning-s08-q02

Each term is multiplied by 3, so the next term is 54 × 3 = 162.

numerical-reasoning-s08-q03

Each term is halved, so the next term is 8 ÷ 2 = 4.

numerical-reasoning-s08-q04

These are the square numbers 1², 2², 3², 4², 5², so the next is 6² = 36.

numerical-reasoning-s08-q05

Each term is the sum of the two before it: 11 + 18 = 29.

numerical-reasoning-s08-q06

The amount subtracted grows by one each step (3, 4, 5, 6), so the next step subtracts 7: 22 − 7 = 15.

numerical-reasoning-s08-q07

Two sequences alternate: the odd positions climb 1, 3, 5, 7 while the even positions fall 10, 8, 6, so the next even-position term is 4.

numerical-reasoning-s08-q08

The gaps grow by one each time (1, 2, 3, 4, 5), so the next gap is 6: 20 + 6 = 26.

numerical-reasoning-s08-q09

8, 27, 64, and 125 are cube numbers (2³, 3³, 4³, 5³); 100 is a square but not a cube.

numerical-reasoning-s08-q10

Apply the rule to 17: 2 × 17 = 34, then 34 − 1 = 33.

numerical-reasoning-s09-q01

First find the capacity: 18 × 22 = 396 seats; then subtract the tickets sold: 396 − 315 = 81.

numerical-reasoning-s09-q02

Remove the fixed fee first: £145 − £40 = £105 of hourly work, then divide by the rate: 105 ÷ 15 = 7 hours.

numerical-reasoning-s09-q03

The trip uses 4.5 × 6 = 27 litres, and 27 × £1.50 = £40.50.

numerical-reasoning-s09-q04

The 20% reduction takes £45 down to £36, and the £5 voucher then brings it to £31. The order of the steps matters.

numerical-reasoning-s09-q05

Their combined age is three equal 'Beth-sized' parts (Beth plus twice Beth), so Beth is 36 ÷ 3 = 12 and Amir is 24.

numerical-reasoning-s09-q06

Work backwards, undoing each step in reverse: 46 − 6 = 40, then 40 ÷ 4 = 10.

numerical-reasoning-s09-q07

Monday's shipment is 15% of 1,200 = 180 units, leaving 1,020; Tuesday's delivery brings it to 1,020 + 250 = 1,270.

numerical-reasoning-s09-q08

The floor area is 4 × 3 = 12 m², needing 12 ÷ 0.25 = 48 tiles, which is 48 ÷ 10 = 4.8, so 5 full boxes must be bought.

numerical-reasoning-s09-q09

The tickets cost 2 × £9 + 3 × £5 = £18 + £15 = £33, so the change is £50 − £33 = £17.

numerical-reasoning-s09-q10

June is 120% of May, so divide rather than take 20% off: 660 ÷ 1.2 = 550. Subtracting 20% of June's figure would give the wrong base.

numerical-reasoning-s10-q01

Apply the multiplier twice: £2,000 × 0.9 × 0.9 = £1,620. The second year's 10% is taken from the reduced value, not the original.

numerical-reasoning-s10-q02

Chain the multipliers: £150 × 0.8 = £120, then £120 × 0.9 = £108. Two successive discounts of 20% and 10% are not the same as one 30% discount.

numerical-reasoning-s10-q03

£96 represents 120% of the original price, so divide by 1.2: 96 ÷ 1.2 = £80. Taking 20% off £96 would use the wrong base.

numerical-reasoning-s10-q04

Work in rates: together they do 1/2 of the job per hour and A alone does 1/3, so B's rate is 1/2 − 1/3 = 1/6 per hour. A full job takes B 6 hours.

numerical-reasoning-s10-q05

More time is spent at the slower speed, so the answer is below the midpoint. For a 120 km leg each way: 2 hours out plus 3 hours back is 240 km in 5 hours = 48 km/h.

numerical-reasoning-s10-q06

A percentage of a percentage multiplies: 40% of 30% is 0.4 × 0.3 = 0.12, which is 12% of all staff.

numerical-reasoning-s10-q07

Round to friendly numbers: 42,000 ÷ 70 = 600, so the quotient is about 600. Estimation is mainly about keeping track of the size of the answer.

numerical-reasoning-q6

Combined rate = 1/4 + 1/6 = 5/12 of the tank per hour, so time = 12/5 = 2.4 hours.

numerical-reasoning-s10-q09

Start from the actual counts: 3 : 2 across 30 counters means 18 red and 12 blue; adding 6 blue gives 18 : 18, which simplifies to 1 : 1.

numerical-reasoning-s10-q10

Multiply the two changes: 1.25 × 0.8 = 1, so the value ends exactly where it started. Percentage rises and falls of different sizes can cancel because they act on different bases.