Learn by Novus · Open practice pack v1

Inductive reasoning: patterns, rules, and generalisation: open practice pack: learner worksheet

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

Ten untimed sections that build from simple sequences to judging the strength of generalisations. Work only from the information given in each prompt. Every item contains all the data you need.

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

Number sequences: single-rule steps

Find the one rule driving each sequence, then choose the next term.

1. inductive-reasoning-s01-q01

What is the next number in the sequence 2, 4, 6, 8, ...?

  1. 9
  2. 10
  3. 12
  4. 14

Answer:

2. inductive-reasoning-s01-q02

What is the next number in the sequence 5, 10, 15, 20, ...?

  1. 21
  2. 24
  3. 25
  4. 30

Answer:

3. inductive-reasoning-s01-q03

What is the next number in the sequence 3, 6, 12, 24, ...?

  1. 30
  2. 36
  3. 42
  4. 48

Answer:

4. inductive-reasoning-s01-q04

What is the next number in the sequence 20, 17, 14, 11, ...?

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

Answer:

5. inductive-reasoning-s01-q05

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

  1. 25
  2. 20
  3. 24
  4. 36

Answer:

6. inductive-reasoning-s01-q06

What is the next number in the sequence 2, 5, 8, 11, ...?

  1. 12
  2. 13
  3. 14
  4. 15

Answer:

7. inductive-reasoning-s01-q07

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

  1. 2
  2. 4
  3. 6
  4. 0

Answer:

8. inductive-reasoning-s01-q08

What is the next number in the sequence 1, 2, 4, 7, 11, ...?

  1. 13
  2. 14
  3. 15
  4. 16

Answer:

9. inductive-reasoning-s01-q09

What is the next number in the sequence 90, 80, 71, 63, ...?

  1. 56
  2. 55
  3. 57
  4. 54

Answer:

10. inductive-reasoning-s01-q10

What is the next number in the sequence 7, 14, 21, 28, ...?

  1. 32
  2. 35
  3. 36
  4. 42

Answer:

Letter patterns and alphabet rules

Treat the alphabet as a numbered line and work out the rule linking the letters.

11. inductive-reasoning-s02-q01

What is the next letter in the sequence A, C, E, G, ...?

  1. H
  2. J
  3. I
  4. K

Answer:

12. inductive-reasoning-s02-q02

What is the next letter in the sequence Z, X, V, T, ...?

  1. R
  2. S
  3. Q
  4. P

Answer:

13. inductive-reasoning-s02-q03

What is the next letter in the sequence B, E, H, K, ...?

  1. M
  2. N
  3. O
  4. L

Answer:

14. inductive-reasoning-s02-q04

What is the next pair in the sequence AZ, BY, CX, DW, ...?

  1. EW
  2. FV
  3. EU
  4. EV

Answer:

15. inductive-reasoning-s02-q05

What is the next letter in the sequence A, B, D, G, K, ...?

  1. N
  2. O
  3. P
  4. Q

Answer:

16. inductive-reasoning-s02-q06

What is the next pair in the sequence CD, FG, IJ, LM, ...?

  1. NO
  2. OP
  3. PQ
  4. MN

Answer:

17. inductive-reasoning-s02-q07

What is the next letter in the sequence A, C, B, D, C, E, D, ...?

  1. F
  2. E
  3. G
  4. C

Answer:

18. inductive-reasoning-s02-q08

What is the next letter in the sequence M, N, L, O, K, P, ...?

  1. I
  2. Q
  3. J
  4. H

Answer:

19. inductive-reasoning-s02-q09

What comes next in the sequence A1, C3, E5, G7, ...?

  1. H8
  2. J9
  3. I8
  4. I9

Answer:

20. inductive-reasoning-s02-q10

Four of these letter pairs follow one rule and one breaks it: BD, EG, HJ, KN, PR. Which pair breaks the rule?

  1. EG
  2. KN
  3. HJ
  4. PR

Answer:

Shape and symbol patterns

Each pattern uses described shapes or symbols: infer the repeating or evolving rule.

21. inductive-reasoning-s03-q01

A pattern repeats: circle, square, triangle, circle, square, ... What shape comes next?

  1. Circle
  2. Square
  3. Star
  4. Triangle

Answer:

22. inductive-reasoning-s03-q02

Symbol sequence: ★ ★ ● ★ ★ ● ★ ... What is the eighth symbol?

  1. ★
  2. ●
  3. ■
  4. It cannot be determined

Answer:

23. inductive-reasoning-s03-q03

An arrow points up, then right, then down, then left, then up, then right. Where does it point next?

  1. Left
  2. Up
  3. Down
  4. Right

Answer:

24. inductive-reasoning-s03-q04

A row of cards shows 1 dot, then 3 dots, then 5 dots, then 7 dots. How many dots are on the next card?

  1. 8
  2. 9
  3. 10
  4. 11

Answer:

25. inductive-reasoning-s03-q05

A pattern alternates: large white square, small black square, large white square, small black square, large white square, ... What comes next?

  1. Small black square
  2. Large white square
  3. Large black square
  4. Small white square

Answer:

26. inductive-reasoning-s03-q06

A series of figures shows a triangle (3 sides), a square (4 sides), a pentagon (5 sides), then a hexagon (6 sides). Which figure comes next?

  1. An octagon (8 sides)
  2. A pentagon (5 sides)
  3. A nonagon (9 sides)
  4. A heptagon (7 sides)

Answer:

27. inductive-reasoning-s03-q07

Symbol groups appear in this order: ○ then ○● then ○●● then ○●●●. What is the next group?

  1. ●●●●○
  2. ○●●●
  3. ○●●●●
  4. ●○●●

Answer:

28. inductive-reasoning-s03-q08

A square tile is shaded one quarter at a time: first the top-left quarter, then the top-right, then the bottom-right. Which quarter is shaded next?

  1. Bottom-left
  2. Top-left
  3. Bottom-right
  4. Top-right

Answer:

29. inductive-reasoning-s03-q09

A series of cards shows: 1 triangle, 2 squares, 3 triangles, 4 squares. What does the next card show?

  1. 5 squares
  2. 5 triangles
  3. 4 triangles
  4. 6 squares

Answer:

30. inductive-reasoning-s03-q10

Four tiles follow one rule and one breaks it: a triangle with 3 dots, a square with 4 dots, a pentagon with 5 dots, and a hexagon with 7 dots. Which tile breaks the rule?

  1. The triangle with 3 dots
  2. The square with 4 dots
  3. The pentagon with 5 dots
  4. The hexagon with 7 dots

Answer:

Classification: find the odd one out

Work out the rule the group shares, then choose the item that does not obey it.

31. inductive-reasoning-s04-q01

Which number does not belong with the others: 8, 64, 100, 216?

  1. 8
  2. 64
  3. 100
  4. 216

Answer:

32. inductive-reasoning-s04-q02

Which word does not belong with the others: letter, coffee, dinner, orange?

  1. letter
  2. coffee
  3. dinner
  4. orange

Answer:

33. inductive-reasoning-s04-q03

Which number does not belong with the others: 27, 35, 45, 63?

  1. 27
  2. 35
  3. 45
  4. 63

Answer:

34. inductive-reasoning-s04-q04

Which letter group does not belong with the others: NPS, BDF, HJL, PRT?

  1. NPS
  2. BDF
  3. HJL
  4. PRT

Answer:

35. inductive-reasoning-s04-q05

Which pair does not belong with the others: (3, 7), (6, 4), (5, 6), (8, 2)?

  1. (3, 7)
  2. (6, 4)
  3. (5, 6)
  4. (8, 2)

Answer:

36. inductive-reasoning-s04-q06

Which word does not belong with the others: level, civic, rotor, tiles?

  1. level
  2. civic
  3. rotor
  4. tiles

Answer:

37. inductive-reasoning-s04-q07

Which number does not belong with the others: 46, 53, 64, 82?

  1. 46
  2. 53
  3. 64
  4. 82

Answer:

38. inductive-reasoning-s04-q08

Which triple does not belong with the others: (3, 6, 12), (5, 10, 20), (4, 8, 12), (7, 14, 28)?

  1. (3, 6, 12)
  2. (5, 10, 20)
  3. (4, 8, 12)
  4. (7, 14, 28)

Answer:

39. inductive-reasoning-s04-q09

Which clock time does not belong with the others: 14:14, 12:21, 15:51, 10:01?

  1. 14:14
  2. 12:21
  3. 15:51
  4. 10:01

Answer:

40. inductive-reasoning-s04-q10

Which group does not belong with the others: (2, 3, 5), (5, 7, 12), (11, 13, 24), (7, 11, 17)?

  1. (2, 3, 5)
  2. (5, 7, 12)
  3. (11, 13, 24)
  4. (7, 11, 17)

Answer:

Analogies: transfer the relation

Work out the relation in the example pair, then apply exactly the same relation to the new case.

41. inductive-reasoning-s05-q01

3 is to 6 as 7 is to ...?

  1. 14
  2. 10
  3. 21
  4. 17

Answer:

42. inductive-reasoning-s05-q02

C is to F as J is to ...?

  1. L
  2. M
  3. N
  4. K

Answer:

43. inductive-reasoning-s05-q03

“stop” is to “pots” as “flow” is to ...?

  1. fowl
  2. low
  3. wolf
  4. flew

Answer:

44. inductive-reasoning-s05-q04

4 is to 16, and 5 is to 25. Following the same rule, 7 is to ...?

  1. 28
  2. 35
  3. 14
  4. 49

Answer:

45. inductive-reasoning-s05-q05

25 is to 5 as 64 is to ...?

  1. 6
  2. 8
  3. 32
  4. 16

Answer:

46. inductive-reasoning-s05-q06

BC is to EF as JK is to ...?

  1. MN
  2. NO
  3. LM
  4. KL

Answer:

47. inductive-reasoning-s05-q07

1/2 is to 2 as 1/8 is to ...?

  1. 4
  2. 16
  3. 1/4
  4. 8

Answer:

48. inductive-reasoning-s05-q08

The pair (3, 5) is to 8 as the pair (7, 6) is to ...?

  1. 12
  2. 13
  3. 42
  4. 1

Answer:

49. inductive-reasoning-s05-q09

A triangle is to 3 as a hexagon is to ...?

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

Answer:

50. inductive-reasoning-s05-q10

In a letter code, CAT is written as DBU. Using the same code, how is DOG written?

  1. EOH
  2. CPF
  3. EPH
  4. DPH

Answer:

Alternating and interleaved sequences

These sequences mix two rules at once: separate the strands before predicting the next term.

51. inductive-reasoning-s06-q01

What is the next number in the sequence 1, 10, 2, 20, 3, 30, 4, ...?

  1. 5
  2. 40
  3. 31
  4. 50

Answer:

52. inductive-reasoning-s06-q02

What is the next number in the sequence 2, 100, 4, 90, 6, 80, ...?

  1. 70
  2. 10
  3. 8
  4. 9

Answer:

53. inductive-reasoning-s06-q03

What is the next number in the sequence 5, 6, 8, 9, 11, 12, ...?

  1. 13
  2. 15
  3. 16
  4. 14

Answer:

54. inductive-reasoning-s06-q04

What comes next in the sequence A, 2, C, 4, E, 6, ...?

  1. G
  2. 8
  3. F
  4. 7

Answer:

55. inductive-reasoning-s06-q05

What is the next number in the sequence 40, 1, 35, 3, 30, 9, 25, ...?

  1. 20
  2. 18
  3. 27
  4. 81

Answer:

56. inductive-reasoning-s06-q06

What is the next number in the sequence 1, 1, 2, 3, 5, 8, ...?

  1. 11
  2. 12
  3. 10
  4. 13

Answer:

57. inductive-reasoning-s06-q07

What is the next number in the sequence 100, 2, 90, 4, 81, 8, 73, ...?

  1. 66
  2. 16
  3. 12
  4. 64

Answer:

58. inductive-reasoning-s06-q08

What comes next in the sequence J, 1, K, 3, M, 6, P, 10, ...?

  1. Q
  2. S
  3. T
  4. U

Answer:

59. inductive-reasoning-s06-q09

What is the next number in the sequence 6, 11, 8, 13, 10, 15, 12, ...?

  1. 17
  2. 14
  3. 16
  4. 19

Answer:

60. inductive-reasoning-s06-q10

What is the next number in the sequence 2, 6, 3, 9, 4.5, 13.5, ...?

  1. 27
  2. 20.25
  3. 7
  4. 6.75

Answer:

Generalising from observations

Read the observations and choose the conclusion they best support, using only what is given.

61. inductive-reasoning-s07-q01

Ana has recorded 47 swan sightings at her local lake this year, and every swan she recorded was white. Which conclusion do her observations best support?

  1. Swans at this lake are usually white.
  2. All swans everywhere are white.
  3. The next swan Ana sees cannot be a different colour.
  4. White is the only possible swan colour.

Answer:

62. inductive-reasoning-s07-q02

A baker notices that rye loaf sales rose on each of the last six rainy Saturdays and fell on each of the last five sunny Saturdays. Which conclusion is best supported?

  1. Rain causes people to crave rye bread.
  2. Rye sales rise on rainy days in every town.
  3. At this bakery, rainy Saturdays have been associated with higher rye sales.
  4. Sunny weather stops people eating bread.

Answer:

63. inductive-reasoning-s07-q03

In a sample of 200 bolts from Machine A, 3 were faulty. In a sample of 200 bolts from Machine B, 21 were faulty. Which conclusion is best supported?

  1. Machine B is broken and must be replaced.
  2. Machine B's output showed a higher fault rate in these samples.
  3. Machine A never produces faulty bolts.
  4. The next bolt from Machine B will certainly be faulty.

Answer:

64. inductive-reasoning-s07-q04

In one garden bed, each of the 12 tomato plants given compost grew taller than each of the 12 plants without compost. Which is the safest reading of this result?

  1. Compost makes all plants grow taller.
  2. The gardener's soil must be unusually poor.
  3. Tomatoes cannot grow well without compost.
  4. In this garden's trial, compost went together with taller growth.

Answer:

65. inductive-reasoning-s07-q05

For five weekdays in a row, the 08:15 bus arrived between 8 and 10 minutes late, while the 08:45 arrived on time. What is the most reasonable expectation for tomorrow?

  1. The 08:15 is likely, though not certain, to be late again.
  2. The 08:15 will be exactly 9 minutes late.
  3. The 08:45 can never run late.
  4. Every bus in the city is unreliable.

Answer:

66. inductive-reasoning-s07-q06

A café surveyed 60 customers and found one in four chose oat milk, but the survey ran only on weekday mornings. Before generalising to all customers, which caution matters most?

  1. Sixty people can never tell you anything useful.
  2. Oat milk drinkers probably avoid surveys.
  3. The sample may not represent afternoon or weekend customers.
  4. The survey should have asked about tea instead.

Answer:

67. inductive-reasoning-s07-q07

A student notices she scored higher on every quiz taken after at least eight hours' sleep than on any quiz taken after less. Which conclusion is best supported?

  1. For this student, more sleep has gone together with higher quiz scores.
  2. Sleep causes high marks for all students.
  3. She is guaranteed a top mark if she sleeps eight hours tonight.
  4. Quizzes taken while tired are unfairly difficult.

Answer:

68. inductive-reasoning-s07-q08

A bag of counters is sampled 300 times (with the counter returned each time): red came out 148 times and blue 152 times. Which inference is most reasonable?

  1. The bag holds exactly 150 red and 150 blue counters.
  2. The bag likely holds red and blue in roughly equal numbers.
  3. The next draw must be red to balance the counts.
  4. Blue counters are heavier than red ones.

Answer:

69. inductive-reasoning-s07-q09

Across four separate climbs, a hiker recorded a temperature drop of about 1°C for every 150 metres of ascent. What should she expect for a 600-metre climb?

  1. A drop of exactly 4.0°C, guaranteed.
  2. A drop of about 2°C.
  3. A drop of roughly 4°C.
  4. No prediction is possible from her records.

Answer:

70. inductive-reasoning-s07-q10

A library's logs show late returns happen most often for books borrowed on Fridays. The logs also show most books are borrowed on Fridays. Which point most weakens the rule 'Friday borrowing causes lateness'?

  1. Some late books were borrowed on Mondays.
  2. The library is closed on Sundays.
  3. Lateness is measured in whole days.
  4. Fridays supply most borrowings overall, so they would lead any count, including late returns, even with no special effect.

Answer:

Grid and matrix patterns

Each grid follows row or column rules: recover them and fill the missing cell.

71. inductive-reasoning-s08-q01

A 3×3 grid reads: row 1: 1, 2, 3; row 2: 4, 5, 6; row 3: 7, 8, ?. What number completes it?

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

Answer:

72. inductive-reasoning-s08-q02

A 3×3 grid reads: row 1: 2, 5, 7; row 2: 3, 6, 9; row 3: 4, 7, ?. What number completes it?

  1. 10
  2. 11
  3. 12
  4. 28

Answer:

73. inductive-reasoning-s08-q03

A 3×3 grid reads: row 1: 2, 3, 5; row 2: 4, 6, 10; row 3: 8, 12, ?. What number completes it?

  1. 20
  2. 15
  3. 24
  4. 18

Answer:

74. inductive-reasoning-s08-q04

A 3×3 grid reads: row 1: 2, 3, 6; row 2: 4, 2, 8; row 3: 3, 5, ?. What number completes it?

  1. 8
  2. 12
  3. 15
  4. 35

Answer:

75. inductive-reasoning-s08-q05

A 3×3 grid of shaded squares reads: row 1: white, grey, black; row 2: black, white, grey; row 3: grey, ?, white. What shade fills the missing cell?

  1. White
  2. Black
  3. Grey
  4. Any shade fits

Answer:

76. inductive-reasoning-s08-q06

A 3×3 grid reads: row 1: 4, 9, 2; row 2: 3, 5, 7; row 3: 8, 1, ?. What number completes it?

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

Answer:

77. inductive-reasoning-s08-q07

A 3×3 grid reads: row 1: 1, 2, 3; row 2: 2, 4, 7; row 3: 3, 7, ?. What number completes it?

  1. 10
  2. 12
  3. 14
  4. 16

Answer:

78. inductive-reasoning-s08-q08

A 3×3 grid of letters reads: row 1: A, D, G; row 2: B, E, H; row 3: C, F, ?. What letter completes it?

  1. I
  2. J
  3. K
  4. H

Answer:

79. inductive-reasoning-s08-q09

A 2×2 grid reads: top row: 6 then 3; bottom row: 10 then ?. What number completes it?

  1. 7
  2. 5
  3. 20
  4. 8

Answer:

80. inductive-reasoning-s08-q10

A 3×3 grid reads: row 1: 9, 4, 5; row 2: 12, 5, 7; row 3: 15, 6, ?. What number completes it?

  1. 8
  2. 11
  3. 10
  4. 9

Answer:

Rule discovery: function machines and codes

Infer the hidden rule that turns each input into its output, then apply it to the new case.

81. inductive-reasoning-s09-q01

A machine turns 3 into 7, 5 into 11, and 8 into 17. What does it turn 10 into?

  1. 21
  2. 20
  3. 19
  4. 25

Answer:

82. inductive-reasoning-s09-q02

A machine turns 4 into 2, 10 into 5, and 16 into 8. What does it turn 26 into?

  1. 24
  2. 52
  3. 12
  4. 13

Answer:

83. inductive-reasoning-s09-q03

In a code, LAMP is written as MBNQ. Using the same code, how is GATE written?

  1. FZSD
  2. HBUF
  3. HAUE
  4. GBTF

Answer:

84. inductive-reasoning-s09-q04

A machine turns 2 into 3, 3 into 5, 5 into 9, and 6 into 11. What does it turn 9 into?

  1. 15
  2. 16
  3. 17
  4. 18

Answer:

85. inductive-reasoning-s09-q05

A code maps 1 to A, 4 to D, and 7 to G. What letter does the same code map 11 to?

  1. K
  2. J
  3. L
  4. I

Answer:

86. inductive-reasoning-s09-q06

A machine turns 5 into 30, 7 into 42, and 9 into 54. What does it turn 11 into?

  1. 60
  2. 72
  3. 55
  4. 66

Answer:

87. inductive-reasoning-s09-q07

A code turns NET into TEN, RAW into WAR, and PIN into NIP. What does it turn BUS into?

  1. USB
  2. BSU
  3. SUB
  4. SBU

Answer:

88. inductive-reasoning-s09-q08

A machine turns 2 into 8, 3 into 27, and 4 into 64. What does it turn 5 into?

  1. 100
  2. 125
  3. 75
  4. 625

Answer:

89. inductive-reasoning-s09-q09

A machine turns 3 into 10, 6 into 19, and 10 into 31. What does it turn 12 into?

  1. 37
  2. 36
  3. 41
  4. 34

Answer:

90. inductive-reasoning-s09-q10

A machine turns 23 into 5, 47 into 11, 65 into 11, and 81 into 9. What does it turn 76 into?

  1. 6
  2. 11
  3. 76
  4. 13

Answer:

Extended extrapolation and inductive strength

These items combine several inductive steps: extrapolate carefully and judge how strong each inference really is.

91. inductive-reasoning-s10-q01

What is the next number in the sequence 4, 6, 10, 18, 34, ...?

  1. 62
  2. 66
  3. 68
  4. 70

Answer:

92. inductive-reasoning-s10-q02

What is the next number in the sequence 2, 6, 12, 20, 30, ...?

  1. 40
  2. 36
  3. 42
  4. 44

Answer:

93. inductive-reasoning-s10-q03

Which of these generalisations rests on the strongest inductive evidence?

  1. A random sample of 1,000 households across a city found 90% recycle weekly, so most households in that city recycle weekly.
  2. Three neighbours on one street recycle, so the whole country recycles.
  3. One street's recycling bins were full on Monday, so everyone recycles.
  4. A recycling firm's advert says most people recycle, so most people do.

Answer:

94. inductive-reasoning-s10-q04

A seedling grew 2 cm in week one, 4 cm in week two, and 8 cm in week three. Someone predicts it will grow 256 cm in week eight by continuing the doubling. What is the main inductive weakness of this prediction?

  1. The arithmetic of the doubling is wrong.
  2. Three weeks is an unusually large sample.
  3. Growth cannot be measured in centimetres.
  4. It assumes a short-run pattern will continue indefinitely without limit.

Answer:

95. inductive-reasoning-s10-q05

A sequence of pairs runs (1, 1), (2, 4), (3, 9), (4, 16), (?, 36). What is the missing first number?

  1. 5
  2. 18
  3. 6
  4. 7

Answer:

96. inductive-reasoning-s10-q06

What is the next number in the sequence 3, 4, 6, 8, 12, 14, 18, 20, ...?

  1. 22
  2. 24
  3. 26
  4. 21

Answer:

97. inductive-reasoning-s10-q07

Researchers have examined 40 beetles near a cave's entrance and all were blind. Which additional observation would most strengthen the generalisation 'all the beetles in this cave are blind'?

  1. Re-examining the same 40 beetles a second time.
  2. Reading that beetles in other caves are often blind.
  3. Counting the legs of the beetles already collected.
  4. Sampling beetles from deep, unexplored parts of the cave and finding them blind too.

Answer:

98. inductive-reasoning-s10-q08

What comes next in the sequence Z1, X2, V4, T8, ...?

  1. R16
  2. S16
  3. R12
  4. Q16

Answer:

99. inductive-reasoning-s10-q09

What is the next number in the sequence 1, 2, 6, 24, 120, ...?

  1. 600
  2. 720
  3. 620
  4. 840

Answer:

100. inductive-reasoning-s10-q10

A sequence runs 2, 4, 8, 14, 22. Which rule fits every step of the sequence?

  1. Each term is double the previous term.
  2. Each term adds 2 to the previous term.
  3. The amount added grows by 2 each step.
  4. Each term is its position number squared.

Answer: