Learn by Novus · Open practice pack v1

Abstract reasoning: patterns, rules and transformations: 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

Every pattern in this bank is described in words, so all the information you need is in the prompt itself. Work at a comfortable pace. The aim is to notice the rule, not to race the clock.

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

Continuing simple sequences

Spot the single repeating or stepping rule and choose what comes next.

1. abstract-reasoning-s01-q01

A sequence runs: circle, square, circle, square, circle. What comes next?

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

Answer:

2. abstract-reasoning-s01-q02

A shape repeats in three sizes: small, medium, large, small, medium. What comes next?

  1. Small
  2. Medium
  3. Large
  4. Extra large

Answer:

3. abstract-reasoning-s01-q03

A letter sequence runs: A, C, E, G. Which letter comes next?

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

Answer:

4. abstract-reasoning-s01-q04

A star pattern grows: ★, ★★, ★★★. Which group comes next?

  1. ★★
  2. ★★★
  3. ★★★★

Answer:

5. abstract-reasoning-s01-q05

An arrow turns through the sequence: up, right, down, left, up, right. Which direction comes next?

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

Answer:

6. abstract-reasoning-s01-q06

A dot pattern runs: ●, ●, ○, ●, ●, ○, ●, ●. What comes next?

  1. ●●
  2. ○○

Answer:

7. abstract-reasoning-s01-q07

A letter sequence runs backwards through the alphabet: Z, X, V, T. Which letter comes next?

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

Answer:

8. abstract-reasoning-s01-q08

A symbol sequence runs: moon, star, sun, moon, star, sun, moon, star. What comes next?

  1. Moon
  2. Star
  3. Cloud
  4. Sun

Answer:

9. abstract-reasoning-s01-q09

A shape sequence gains one side each step: triangle, square, pentagon. Which shape comes next?

  1. Heptagon
  2. Octagon
  3. Hexagon
  4. Circle

Answer:

10. abstract-reasoning-s01-q10

A dot pattern doubles each step: 1 dot, 2 dots, 4 dots, 8 dots. How many dots come next?

  1. 10 dots
  2. 16 dots
  3. 12 dots
  4. 24 dots

Answer:

Odd one out: classifying by a shared rule

Find the feature three of the four share, then pick the one that breaks it.

11. abstract-reasoning-s02-q01

Which of these shapes does not belong with the other three?

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

Answer:

12. abstract-reasoning-s02-q02

Which of these capital letters does not belong with the other three?

  1. S
  2. X
  3. K
  4. T

Answer:

13. abstract-reasoning-s02-q03

Which of these capital letters does not belong with the other three?

  1. A
  2. H
  3. F
  4. M

Answer:

14. abstract-reasoning-s02-q04

Which of these does not belong with the other three?

  1. Cube
  2. Square
  3. Sphere
  4. Cylinder

Answer:

15. abstract-reasoning-s02-q05

Which of these letter pairs does not belong with the other three?

  1. AB
  2. XX
  3. AA
  4. MM

Answer:

16. abstract-reasoning-s02-q06

Which of these codes does not belong with the other three?

  1. A1
  2. B2
  3. C3
  4. 4D

Answer:

17. abstract-reasoning-s02-q07

Which of these shapes does not belong with the other three?

  1. Triangle
  2. Hexagon
  3. Pentagon
  4. Heptagon

Answer:

18. abstract-reasoning-s02-q08

Which of these letters does not belong with the other three?

  1. B
  2. D
  3. K
  4. H

Answer:

19. abstract-reasoning-s02-q09

Which of these symbol groups does not belong with the other three?

  1. ★★
  2. ▲▲▲
  3. ●●●
  4. ■■■

Answer:

20. abstract-reasoning-s02-q10

Which of these capital letters does not belong with the other three?

  1. S
  2. N
  3. E
  4. Z

Answer:

Alternating and repeating cycles

These patterns repeat in fixed cycles. Work out the cycle length before answering.

21. abstract-reasoning-s03-q01

In a sequence, the shape alternates circle/square while the colour cycles red, blue, green. So far: red circle, blue square, green circle, red square, blue circle. What comes next?

  1. Red square
  2. Green circle
  3. Green square
  4. Blue square

Answer:

22. abstract-reasoning-s03-q02

An arrow cycles: up, right, down, up, right, down, up. Which direction comes next?

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

Answer:

23. abstract-reasoning-s03-q03

A marker on a clock face jumps three hours clockwise each step: 12, 3, 6, 9. Where does it land next?

  1. 3
  2. 6
  3. 9
  4. 12

Answer:

24. abstract-reasoning-s03-q04

A letter sequence runs: A, B, A, C, A, D, A. Which letter comes next?

  1. E
  2. A
  3. F
  4. B

Answer:

25. abstract-reasoning-s03-q05

In a sequence, the triangle flips each step while the shading changes every two steps. So far: black ▲, black ▼, white ▲, white ▼, black ▲. What comes next?

  1. White ▼
  2. Black ▲
  3. Black ▼
  4. White ▲

Answer:

26. abstract-reasoning-s03-q06

The four suits repeat in a fixed order: ♠, ♥, ♦, ♣, ♠, ♥, ♦, ♣, and so on. Which symbol is 10th in the sequence?

Answer:

27. abstract-reasoning-s03-q07

The numbers 1, 2, 3 repeat forever: 1, 2, 3, 1, 2, 3, … What is the 12th term?

  1. 3
  2. 1
  3. 2
  4. It cannot be determined

Answer:

28. abstract-reasoning-s03-q08

A pattern runs: ●, ■, ●●, ■■, ●●●. What comes next?

  1. ●●●●
  2. ■■
  3. ●●●
  4. ■■■

Answer:

29. abstract-reasoning-s03-q09

A pendulum pattern runs: left, centre, right, centre, left, centre, right. What comes next?

  1. Left
  2. Right
  3. It cannot be determined
  4. Centre

Answer:

30. abstract-reasoning-s03-q10

A sequence cycles the letters X, Y, Z while alternating upper and lower case: X, y, Z, x, Y, z, X. What comes next?

  1. Y
  2. y
  3. z
  4. x

Answer:

Growing and shrinking patterns

Work out how much the pattern grows or shrinks at each step. The step size itself may change.

31. abstract-reasoning-s04-q01

A dot pattern grows: 1 dot, 3 dots, 5 dots, 7 dots. How many dots come next?

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

Answer:

32. abstract-reasoning-s04-q02

A block pattern shrinks: 10 blocks, 8 blocks, 6 blocks, 4 blocks. How many blocks come next?

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

Answer:

33. abstract-reasoning-s04-q03

A tile pattern grows: 1, 2, 4, 7, 11. How many tiles come next?

  1. 15
  2. 16
  3. 14
  4. 18

Answer:

34. abstract-reasoning-s04-q04

A cell pattern doubles: 2, 4, 8, 16. How many cells come next?

  1. 24
  2. 20
  3. 32
  4. 30

Answer:

35. abstract-reasoning-s04-q05

A dot pattern halves: 64, 32, 16, 8. How many dots come next?

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

Answer:

36. abstract-reasoning-s04-q06

A counter pattern runs: 3, 6, 5, 10, 9, 18. What comes next?

  1. 17
  2. 36
  3. 19
  4. 20

Answer:

37. abstract-reasoning-s04-q07

Dots are arranged in ever-larger square grids: 1 dot, 4 dots, 9 dots, 16 dots. How many dots come next?

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

Answer:

38. abstract-reasoning-s04-q08

Dots are stacked in triangles, adding one more dot per new row: 1, 3, 6, 10. How many dots come next?

  1. 14
  2. 15
  3. 16
  4. 20

Answer:

39. abstract-reasoning-s04-q09

A pattern rises and falls: 5, 8, 6, 9, 7, 10. What comes next?

  1. 11
  2. 9
  3. 12
  4. 8

Answer:

40. abstract-reasoning-s04-q10

In a spiral pattern, each new count is the sum of the previous two: 1, 1, 2, 3, 5, 8. What comes next?

  1. 13
  2. 12
  3. 16
  4. 11

Answer:

Shape and symbol analogies

Work out how the first pair is related, then apply exactly the same relationship to the second.

41. abstract-reasoning-s05-q01

Small circle is to large circle as small square is to what?

  1. Large circle
  2. Large square
  3. Small triangle
  4. Large triangle

Answer:

42. abstract-reasoning-s05-q02

The lower-case letter b is to d as p is to what? (Think of each pair as mirror images.)

  1. q
  2. g
  3. b
  4. o

Answer:

43. abstract-reasoning-s05-q03

3 is to triangle as 6 is to what?

  1. Pentagon
  2. Octagon
  3. Heptagon
  4. Hexagon

Answer:

44. abstract-reasoning-s05-q04

Black square is to white square as black circle is to what?

  1. White square
  2. Black triangle
  3. White circle
  4. Grey circle

Answer:

45. abstract-reasoning-s05-q05

AB is to BA as CD is to what?

  1. CD
  2. DC
  3. CC
  4. DD

Answer:

46. abstract-reasoning-s05-q06

Circle is to sphere as square is to what?

  1. Cylinder
  2. Pyramid
  3. Cone
  4. Cube

Answer:

47. abstract-reasoning-s05-q07

3 is to 6 as 5 is to what?

  1. 10
  2. 15
  3. 25
  4. 8

Answer:

48. abstract-reasoning-s05-q08

A is to C as M is to what?

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

Answer:

49. abstract-reasoning-s05-q09

XOX is to OXO as ABA is to what?

  1. ABA
  2. AAB
  3. BAB
  4. BBA

Answer:

50. abstract-reasoning-s05-q10

▲▲● is to ●▲▲ as ■■★ is to what?

  1. ■★■
  2. ■■★
  3. ★★■
  4. ★■■

Answer:

Symbol operators and transformations

Each item defines an operator in the prompt. Apply it exactly as described.

51. abstract-reasoning-s06-q01

The operator → reverses a string of symbols. What is KLM → ?

  1. KML
  2. LKM
  3. MLK
  4. MKL

Answer:

52. abstract-reasoning-s06-q02

The operator ◇ swaps only the first and last symbols of a string. What is ◇ applied to 2589?

  1. 9852
  2. 5289
  3. 8529
  4. 9582

Answer:

53. abstract-reasoning-s06-q03

The operator # doubles every symbol: #(AB) = AABB. What is #(XY)?

  1. XXYY
  2. XYXY
  3. XY
  4. YYXX

Answer:

54. abstract-reasoning-s06-q04

The operator ∆ removes every second symbol: ∆(ABCDE) = ACE. What is ∆(PQRST)?

  1. QS
  2. PRT
  3. PQR
  4. QST

Answer:

55. abstract-reasoning-s06-q05

A rule shifts each letter one place forward in the alphabet (A becomes B). Apply it to the letters C, F, K.

  1. D, G, L
  2. B, E, J
  3. D, G, K
  4. E, H, M

Answer:

56. abstract-reasoning-s06-q06

The operator ◇ swaps the first and last symbols; the operator # doubles every symbol. What is #(◇(ABC))?

  1. AABBCC
  2. CBACBA
  3. CCBBAA
  4. AACCBB

Answer:

57. abstract-reasoning-s06-q07

The operator ★ rotates a string one position left: ★(ABCD) = BCDA. What is ★(★(WXYZ))?

  1. XYZW
  2. ZWXY
  3. WXYZ
  4. YZWX

Answer:

58. abstract-reasoning-s06-q08

A rule replaces shapes in a cycle: ○ becomes □, □ becomes △, and △ becomes ○. If the rule is applied twice to ○, what results?

Answer:

59. abstract-reasoning-s06-q09

The operator ! reverses a string; the operator @ removes the first symbol. What is @(!(1234))?

  1. 432
  2. 321
  3. 234
  4. 123

Answer:

60. abstract-reasoning-s06-q10

The operator M appends a string's reverse to itself: M(AB) = ABBA. What is M(XY)?

  1. XYYX
  2. YXXY
  3. XXYY
  4. XYXY

Answer:

Matrix reasoning: rules across rows and columns

Each item describes a 3×3 grid. Find the rule running along its rows or columns to fill the gap.

61. abstract-reasoning-s07-q01

In a 3×3 grid, every row contains one circle, one square and one triangle in some order. Row 3 so far reads: square, triangle, blank. What fills the blank?

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

Answer:

62. abstract-reasoning-s07-q02

In a 3×3 grid, the number of dots in each row increases by one from left to right. Row 3 starts with 4 dots. How many dots are in its middle cell?

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

Answer:

63. abstract-reasoning-s07-q03

In a 3×3 grid, row 1 reads black, grey, white and row 2 reads grey, white, black. Row 3 reads white, black, blank. What shade fills the blank?

  1. Black
  2. White
  3. Grey
  4. It cannot be determined

Answer:

64. abstract-reasoning-s07-q04

In a 3×3 grid, the third cell of each row shows the first two cells' contents combined into one figure. Row 3's first cell holds a vertical line and its second cell holds a horizontal line. What does its third cell show?

  1. A cross (both lines together)
  2. A vertical line only
  3. A horizontal line only
  4. An empty cell

Answer:

65. abstract-reasoning-s07-q05

In a 3×3 grid, each row and each column contains exactly one star. The stars sit at row 1 column 2 and row 2 column 3. In which column is row 3's star?

  1. Column 2
  2. Column 3
  3. Any column
  4. Column 1

Answer:

66. abstract-reasoning-s07-q06

In a 3×3 grid, shapes gain one side moving left to right along each row. Row 3 reads: pentagon, hexagon, blank. What fills the blank?

  1. Octagon
  2. Hexagon
  3. Heptagon
  4. Nonagon

Answer:

67. abstract-reasoning-s07-q07

In a 3×3 grid, arrows rotate 90° clockwise moving left to right along each row. Row 3's first arrow points left. Where does its middle arrow point?

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

Answer:

68. abstract-reasoning-s07-q08

In a 3×3 grid, the number of dots in each cell equals its row number multiplied by its column number. How many dots are in the bottom-right cell (row 3, column 3)?

  1. 9
  2. 6
  3. 8
  4. 12

Answer:

69. abstract-reasoning-s07-q09

In a 3×3 grid, the third cell of each row shows only the shapes appearing in exactly one of the first two cells. Row 3's first cell holds a circle and a square; its second cell holds a square and a triangle. What does its third cell show?

  1. A square only
  2. A circle and a triangle
  3. A circle, a square and a triangle
  4. A square and a triangle

Answer:

70. abstract-reasoning-s07-q10

In a 3×3 grid, every row and every column contains one small, one medium and one large shape. Row 1 reads small, medium, large; row 2 reads medium, large, small. Row 3 reads large, small, blank. What size fills the blank?

  1. Small
  2. Large
  3. Medium
  4. It cannot be determined

Answer:

Interleaved sequences: two patterns in one

Each sequence weaves two or more independent strands together, separate them before answering.

71. abstract-reasoning-s08-q01

A sequence runs: 1, 10, 2, 20, 3, 30, 4. What comes next?

  1. 40
  2. 5
  3. 35
  4. 50

Answer:

72. abstract-reasoning-s08-q02

A sequence runs: A, Z, B, Y, C, X. What comes next?

  1. W
  2. E
  3. D
  4. Y

Answer:

73. abstract-reasoning-s08-q03

A sequence runs: ▲, A, ▲▲, B, ▲▲▲, C. What comes next?

  1. D
  2. ▲▲▲▲
  3. ▲▲▲
  4. ▲▲▲▲▲

Answer:

74. abstract-reasoning-s08-q04

A sequence runs: 2, 3, 4, 6, 6, 9, 8. What comes next?

  1. 10
  2. 9
  3. 11
  4. 12

Answer:

75. abstract-reasoning-s08-q05

A sequence runs: Z, 1, X, 2, V, 4, T, 8. What comes next?

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

Answer:

76. abstract-reasoning-s08-q06

A sequence runs: ●, ■■, ●●●, ■■■■, ●●●●●. What comes next?

  1. ■■■■■■
  2. ●●●●●●
  3. ■■■■■
  4. ●●●●●●●

Answer:

77. abstract-reasoning-s08-q07

A sequence runs: 1, 2, 4, 3, 9, 4, 16, 5. What comes next?

  1. 20
  2. 6
  3. 36
  4. 25

Answer:

78. abstract-reasoning-s08-q08

A sequence of codes runs: A1, C3, E5, G7. What comes next?

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

Answer:

79. abstract-reasoning-s08-q09

A sequence runs: 1, A, ●, 2, B, ●●, 3, C. What comes next?

  1. 4
  2. D
  3. ●●
  4. ●●●

Answer:

80. abstract-reasoning-s08-q10

A sequence runs: 100, 1, 90, 2, 80, 4, 70, 8. What comes next?

  1. 60
  2. 16
  3. 50
  4. 10

Answer:

Rule induction: infer the hidden rule

A 'machine' transforms inputs into outputs: infer its hidden rule from the examples, then apply it.

81. abstract-reasoning-s09-q01

A machine transforms: 12 into 21, 47 into 74, and 58 into 85. What does it turn 39 into?

  1. 40
  2. 93
  3. 36
  4. 39

Answer:

82. abstract-reasoning-s09-q02

A machine transforms: ABC into BCD, and HIJ into IJK. What does it turn PQR into?

  1. OPQ
  2. PQS
  3. RST
  4. QRS

Answer:

83. abstract-reasoning-s09-q03

A machine transforms: 3 into 10, 5 into 16, and 7 into 22. What does it turn 9 into?

  1. 28
  2. 27
  3. 30
  4. 25

Answer:

84. abstract-reasoning-s09-q04

A machine transforms: AB into ABB, and CD into CDD. What does it turn XY into?

  1. XXY
  2. XYXY
  3. XYY
  4. XY

Answer:

85. abstract-reasoning-s09-q05

A machine transforms: 25 into 7, 63 into 9, and 48 into 12. What does it turn 57 into?

  1. 12
  2. 35
  3. 13
  4. 11

Answer:

86. abstract-reasoning-s09-q06

A machine transforms: ●●●● into ●●, and ●●●●●● into ●●●. What does it turn ●●●●●●●● into?

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

Answer:

87. abstract-reasoning-s09-q07

A machine transforms: square into triangle, pentagon into square, and hexagon into pentagon. What does it turn a heptagon into?

  1. Octagon
  2. Pentagon
  3. Hexagon
  4. Heptagon

Answer:

88. abstract-reasoning-s09-q08

A machine takes a pair of numbers: (2, 3) gives 8, (3, 4) gives 14, and (4, 5) gives 22. What does (5, 6) give?

  1. 30
  2. 28
  3. 34
  4. 32

Answer:

89. abstract-reasoning-s09-q09

A machine transforms: A into 1, D into 4, and J into 10. What does it turn Q into?

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

Answer:

90. abstract-reasoning-s09-q10

A machine answers YES to 121, 3443 and 78987, and NO to 123 and 3442. Which of these new inputs would it answer YES to?

  1. 45653
  2. 45664
  3. 45674
  4. 45654

Answer:

Combined and multi-step rules

These items chain several rules together. Track the intermediate result after every step.

91. abstract-reasoning-s10-q01

The operator R reverses a string; the operator D deletes its last symbol. Working from the inside out, what is D(R(58274))?

  1. 8274
  2. 5827
  3. 4728
  4. 47285

Answer:

92. abstract-reasoning-s10-q02

A token sits at position 1 of a circle of eight positions numbered 1 to 8. Each step it moves forward three positions, wrapping past 8 back to 1. Where is it after five steps?

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

Answer:

93. abstract-reasoning-s10-q03

A counter starts at 5. The rule alternates: first double, then subtract 3, then double, and so on. What is the counter after four steps?

  1. 14
  2. 17
  3. 7
  4. 11

Answer:

94. abstract-reasoning-s10-q04

Apply two rules in order to the letters ACE: first shift every letter two places forward in the alphabet, then reverse the whole string. What results?

  1. CEG
  2. GEC
  3. ECA
  4. ACG

Answer:

95. abstract-reasoning-s10-q05

A token starts white and flips colour (white to black or black to white) every time it passes a gate. It passes three gates of type P, which each flip it once, and two gates of type Q, which each flip it twice. What colour is it at the end?

  1. White
  2. It depends on the order of the gates
  3. It cannot be determined
  4. Black

Answer:

96. abstract-reasoning-s10-q06

In each row of a 3×3 grid, the middle cell shows the left cell rotated 90° clockwise, and the right cell shows the middle cell rotated 90° clockwise again. Row 3's left cell is an arrow pointing left. Where does its right cell's arrow point?

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

Answer:

97. abstract-reasoning-s10-q07

A sequence runs: 3, 4, 6, 10, 18. What comes next?

  1. 34
  2. 26
  3. 30
  4. 36

Answer:

98. abstract-reasoning-s10-q08

A sequence runs: 2, 6, 12, 20, 30. What comes next?

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

Answer:

99. abstract-reasoning-s10-q09

A code rule shifts every letter one place back in the alphabet and doubles every digit: C4F2 becomes B8E4. What does D3H5 become?

  1. C6G10
  2. E6I10
  3. C6G1
  4. D6H10

Answer:

100. abstract-reasoning-s10-q10

The operator # doubles every symbol (#(AB) = AABB); the operator ∆ removes every second symbol (∆(ABCD) = AC). What is ∆(#(AB))?

  1. AABB
  2. AB
  3. BA
  4. An empty string

Answer: