Learn by Novus · Open practice pack v1

Abstract reasoning: patterns, rules and transformations: 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

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. ★★★
  4. ★★★★

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. ●
  3. ●●
  4. ○○

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?

  1. ♠
  2. ♥
  3. ♦
  4. ♣

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?

  1. □
  2. △
  3. ○
  4. ◇

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:

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
abstract-reasoning-s01-q01BSquare
abstract-reasoning-s01-q02CLarge
abstract-reasoning-s01-q03AI
abstract-reasoning-s01-q04D★★★★
abstract-reasoning-s01-q05BDown
abstract-reasoning-s01-q06A○
abstract-reasoning-s01-q07CR
abstract-reasoning-s01-q08DSun
abstract-reasoning-s01-q09CHexagon
abstract-reasoning-s01-q10B16 dots
abstract-reasoning-s02-q01DCircle
abstract-reasoning-s02-q02AS
abstract-reasoning-s02-q03CF
abstract-reasoning-s02-q04BSquare
abstract-reasoning-s02-q05AAB
abstract-reasoning-s02-q06D4D
abstract-reasoning-s02-q07BHexagon
abstract-reasoning-s02-q08CK
abstract-reasoning-s02-q09A★★
abstract-reasoning-s02-q10CE
abstract-reasoning-s03-q01CGreen square
abstract-reasoning-s03-q02BRight
abstract-reasoning-s03-q03D12
abstract-reasoning-s03-q04AE
abstract-reasoning-s03-q05CBlack ▼
abstract-reasoning-s03-q06B♥
abstract-reasoning-s03-q07A3
abstract-reasoning-s03-q08D■■■
abstract-reasoning-s03-q09DCentre
abstract-reasoning-s03-q10By
abstract-reasoning-s04-q01A9
abstract-reasoning-s04-q02D2
abstract-reasoning-s04-q03B16
abstract-reasoning-s04-q04C32
abstract-reasoning-s04-q05D4
abstract-reasoning-s04-q06A17
abstract-reasoning-s04-q07C25
abstract-reasoning-s04-q08B15
abstract-reasoning-s04-q09D8
abstract-reasoning-s04-q10A13
abstract-reasoning-s05-q01BLarge square
abstract-reasoning-s05-q02Aq
abstract-reasoning-s05-q03DHexagon
abstract-reasoning-s05-q04CWhite circle
abstract-reasoning-s05-q05BDC
abstract-reasoning-s05-q06DCube
abstract-reasoning-s05-q07A10
abstract-reasoning-s05-q08CO
abstract-reasoning-s05-q09CBAB
abstract-reasoning-s05-q10D★■■
abstract-reasoning-s06-q01CMLK
abstract-reasoning-s06-q02D9582
abstract-reasoning-s06-q03AXXYY
abstract-reasoning-s06-q04BPRT
abstract-reasoning-s06-q05AD, G, L
abstract-reasoning-s06-q06CCCBBAA
abstract-reasoning-s06-q07DYZWX
abstract-reasoning-s06-q08B△
abstract-reasoning-s06-q09B321
abstract-reasoning-s06-q10AXYYX
abstract-reasoning-s07-q01DCircle
abstract-reasoning-s07-q02B5
abstract-reasoning-s07-q03CGrey
abstract-reasoning-s07-q04AA cross (both lines together)
abstract-reasoning-s07-q05DColumn 1
abstract-reasoning-s07-q06CHeptagon
abstract-reasoning-s07-q07BUp
abstract-reasoning-s07-q08A9
abstract-reasoning-s07-q09BA circle and a triangle
abstract-reasoning-s07-q10CMedium
abstract-reasoning-s08-q01A40
abstract-reasoning-s08-q02CD
abstract-reasoning-s08-q03B▲▲▲▲
abstract-reasoning-s08-q04D12
abstract-reasoning-s08-q05CR
abstract-reasoning-s08-q06A■■■■■■
abstract-reasoning-s08-q07D25
abstract-reasoning-s08-q08BI9
abstract-reasoning-s08-q09D●●●
abstract-reasoning-s08-q10A60
abstract-reasoning-s09-q01B93
abstract-reasoning-s09-q02DQRS
abstract-reasoning-s09-q03A28
abstract-reasoning-s09-q04CXYY
abstract-reasoning-s09-q05A12
abstract-reasoning-s09-q06B●●●●
abstract-reasoning-s09-q07CHexagon
abstract-reasoning-s09-q08D32
abstract-reasoning-s09-q09C17
abstract-reasoning-s09-q10D45654
abstract-reasoning-s10-q01C4728
abstract-reasoning-s10-q02APosition 8
abstract-reasoning-s10-q03D11
abstract-reasoning-s10-q04BGEC
abstract-reasoning-s10-q05DBlack
abstract-reasoning-s10-q06BRight
abstract-reasoning-s10-q07A34
abstract-reasoning-s10-q08C42
abstract-reasoning-s10-q09AC6G10
abstract-reasoning-s10-q10BAB

Worked explanations

abstract-reasoning-s01-q01

The sequence simply alternates between two shapes, so after a circle the square returns.

abstract-reasoning-s01-q02

The three sizes cycle in a fixed order, so after medium the cycle continues with large.

abstract-reasoning-s01-q03

Each step skips exactly one letter of the alphabet, so G is followed by I.

abstract-reasoning-s01-q04

Each group adds one more star than the last, so three stars are followed by four.

abstract-reasoning-s01-q05

The arrow rotates a quarter turn clockwise each step through a four-direction cycle, so after right it points down.

abstract-reasoning-s01-q06

The repeating block is two black dots followed by one white dot, so the white dot is due next.

abstract-reasoning-s01-q07

Each step moves two letters backwards through the alphabet, so T is followed by R.

abstract-reasoning-s01-q08

The three symbols repeat in a fixed cycle, and the cycle has reached the sun's turn.

abstract-reasoning-s01-q09

The side count climbs 3, 4, 5, so the next shape has six sides, a hexagon.

abstract-reasoning-s01-q10

Each group has twice as many dots as the one before, so 8 doubles to 16.

abstract-reasoning-s02-q01

Three of the shapes are built entirely from straight sides; the circle is the only curved shape.

abstract-reasoning-s02-q02

X, K and T are drawn with straight strokes only, while S is drawn entirely with curves.

abstract-reasoning-s02-q03

A, H and M each have a vertical line of symmetry, their left and right halves mirror each other, but F does not.

abstract-reasoning-s02-q04

Cube, sphere and cylinder are solid three-dimensional forms; the square is a flat two-dimensional shape.

abstract-reasoning-s02-q05

Three of the pairs repeat the same letter twice; only one pairs two different letters.

abstract-reasoning-s02-q06

Three codes place a letter before its matching digit; one reverses the order and puts the digit first.

abstract-reasoning-s02-q07

The triangle, pentagon and heptagon have odd numbers of sides (3, 5, 7); the hexagon's six sides make it the only even one.

abstract-reasoning-s02-q08

B, D and H sit at alphabet positions 2, 4 and 8, each double the last, while K sits at position 11.

abstract-reasoning-s02-q09

Three groups contain exactly three identical symbols; the star group contains only two.

abstract-reasoning-s02-q10

S, N and Z look the same after a half-turn (180° rotation), but E does not share this rotational symmetry.

abstract-reasoning-s03-q01

Track each feature separately: the shape alternates, so a square is due; the colour cycle red-blue-green has reached green.

abstract-reasoning-s03-q02

The cycle is three directions long (up, right, down), and after up the cycle continues with right.

abstract-reasoning-s03-q03

Three hours past 9 wraps around the clock face back to 12, completing the four-step cycle.

abstract-reasoning-s03-q04

The sequence alternates between a fixed A and a letter that advances one step each visit (B, C, D), so E is due.

abstract-reasoning-s03-q05

The two features run at different speeds: the triangle flips every step (so ▼ is due) while the shading holds for two steps (so black continues).

abstract-reasoning-s03-q06

The cycle is four symbols long, so position 10 = two full cycles (8) plus 2 more, the second symbol of the cycle.

abstract-reasoning-s03-q07

Position 12 is exactly four complete cycles of three, so it lands on the final term of a cycle.

abstract-reasoning-s03-q08

The shapes alternate circle/square while the count rises by one each pair, so three squares follow three circles.

abstract-reasoning-s03-q09

The pendulum passes through the centre between every swing to a side, so centre always follows left or right.

abstract-reasoning-s03-q10

Run the two cycles separately: the letter cycle X-Y-Z has reached Y, and the case alternation has reached lower case.

abstract-reasoning-s04-q01

Each group adds two dots to the last, so 7 grows to 9.

abstract-reasoning-s04-q02

The pattern loses two blocks each step, so 4 shrinks to 2.

abstract-reasoning-s04-q03

The amount added grows by one each step (+1, +2, +3, +4), so the next step adds 5 to reach 16.

abstract-reasoning-s04-q04

Each count is twice the one before, so 16 doubles to 32.

abstract-reasoning-s04-q05

Each count is half the one before, so 8 halves to 4.

abstract-reasoning-s04-q06

Two rules alternate: double, then subtract one. After doubling 9 to 18, the next step subtracts one to give 17.

abstract-reasoning-s04-q07

The counts are square grids of side 1, 2, 3, 4, so the next grid is 5 × 5 = 25 dots.

abstract-reasoning-s04-q08

Each triangle adds a new bottom row one dot longer than the last (+2, +3, +4), so the next step adds 5 to reach 15.

abstract-reasoning-s04-q09

The rule alternates +3 then −2. After adding 3 to reach 10, the next step subtracts 2 to give 8.

abstract-reasoning-s04-q10

Adding the last two counts, 5 + 8, gives 13.

abstract-reasoning-s05-q01

The relationship enlarges the shape without changing it, so the square simply becomes large.

abstract-reasoning-s05-q02

b and d are left-right mirror images of each other, and the mirror image of p is q.

abstract-reasoning-s05-q03

The number names how many sides the shape has, and the six-sided shape is the hexagon.

abstract-reasoning-s05-q04

The relationship swaps the shading from black to white while keeping the shape the same.

abstract-reasoning-s05-q05

The relationship reverses the order of the two symbols, so CD becomes DC.

abstract-reasoning-s05-q06

The relationship turns a flat shape into its three-dimensional counterpart, and the solid built from squares is the cube.

abstract-reasoning-s05-q07

The relationship doubles the first number, and 5 doubled is 10.

abstract-reasoning-s05-q08

The relationship moves two places forward in the alphabet, and two letters after M comes O.

abstract-reasoning-s05-q09

The relationship swaps the roles of the two symbols: the outer symbol moves to the middle and vice versa.

abstract-reasoning-s05-q10

The relationship moves the last symbol to the front of the group, so the star leads the two squares.

abstract-reasoning-s06-q01

Reversing writes the symbols in the opposite order, so the last letter comes first.

abstract-reasoning-s06-q02

Only the outer symbols trade places, 2 and 9 swap, while the middle symbols 5 and 8 stay put.

abstract-reasoning-s06-q03

Each symbol is written twice in place before moving to the next, following the worked example exactly.

abstract-reasoning-s06-q04

The operator keeps the 1st, 3rd and 5th symbols and drops the 2nd and 4th, just as in the worked example.

abstract-reasoning-s06-q05

Each letter moves forward exactly one place: C to D, F to G, K to L.

abstract-reasoning-s06-q06

Work from the inside out: swapping first and last turns ABC into CBA, then doubling each symbol gives CCBBAA.

abstract-reasoning-s06-q07

Each rotation moves the front symbol to the back: WXYZ becomes XYZW, then XYZW becomes YZWX.

abstract-reasoning-s06-q08

Follow the cycle one step at a time: the circle first becomes a square, and the square then becomes a triangle.

abstract-reasoning-s06-q09

Reversing 1234 gives 4321, and removing the first symbol of that result leaves 321.

abstract-reasoning-s06-q10

The original string XY is followed by its reverse YX, producing a mirror-symmetric result.

abstract-reasoning-s07-q01

Each row must contain all three shapes exactly once, and the circle is the one still missing from row 3.

abstract-reasoning-s07-q02

Moving one cell to the right adds one dot, so the middle cell holds 4 + 1 = 5 dots.

abstract-reasoning-s07-q03

Each row shifts the previous row one place to the left, so row 3 continues white, black, grey, and grey also completes its column.

abstract-reasoning-s07-q04

Combining the two cells overlays their contents, and a vertical line laid over a horizontal line forms a cross.

abstract-reasoning-s07-q05

Columns 2 and 3 already have their single star, so row 3's star must occupy the only remaining column.

abstract-reasoning-s07-q06

The side count rises 5, 6 along the row, so the final cell holds the seven-sided heptagon.

abstract-reasoning-s07-q07

A quarter turn clockwise carries a left-pointing arrow round to point up.

abstract-reasoning-s07-q08

Applying the stated rule to the bottom-right cell gives 3 × 3 = 9 dots.

abstract-reasoning-s07-q09

The square appears in both cells so it is excluded, leaving the circle and triangle, which each appear only once.

abstract-reasoning-s07-q10

Row 3 already has large and small, so medium completes the row, and it also completes the third column, which holds large and small so far.

abstract-reasoning-s08-q01

Two strands alternate: 1, 2, 3, 4 and 10, 20, 30. The next term belongs to the tens strand.

abstract-reasoning-s08-q02

One strand climbs from the start of the alphabet (A, B, C) while the other descends from the end (Z, Y, X); the climbing strand is due next.

abstract-reasoning-s08-q03

Triangle groups (growing by one) alternate with advancing letters, and it is the triangles' turn with four.

abstract-reasoning-s08-q04

The odd positions climb by two (2, 4, 6, 8) and the even positions climb by three (3, 6, 9); the next term continues the threes with 12.

abstract-reasoning-s08-q05

The letter strand steps back two places each time (Z, X, V, T) while the number strand doubles; the letters are due next with R.

abstract-reasoning-s08-q06

The shapes alternate circle/square while the count rises by one each term, so six squares follow five circles.

abstract-reasoning-s08-q07

The odd positions hold square numbers (1, 4, 9, 16) and the even positions simply count (2, 3, 4, 5); the next square number is 25.

abstract-reasoning-s08-q08

The letters advance two places each step while the digits climb through the odd numbers, giving I paired with 9.

abstract-reasoning-s08-q09

Three strands rotate (a count, a letter, then a dot group that grows by one), and it is the dots' turn with three.

abstract-reasoning-s08-q10

One strand falls by ten (100, 90, 80, 70) while the other doubles (1, 2, 4, 8); the falling strand is due next.

abstract-reasoning-s09-q01

Each example reverses the order of the digits, so 39 becomes 93.

abstract-reasoning-s09-q02

The machine shifts every letter one place forward in the alphabet, so P, Q, R become Q, R, S.

abstract-reasoning-s09-q03

Each output is three times the input plus one, a rule all three examples satisfy, so 9 maps to 28.

abstract-reasoning-s09-q04

The machine repeats only the final symbol, so XY gains a second Y.

abstract-reasoning-s09-q05

Each output is the sum of the input's digits (2+5=7, 6+3=9, 4+8=12), so 5+7 gives 12.

abstract-reasoning-s09-q06

The machine halves the number of dots, so eight dots become four.

abstract-reasoning-s09-q07

Each example removes one side from the shape, so the seven-sided heptagon becomes a six-sided hexagon.

abstract-reasoning-s09-q08

Each output is the pair's product plus two (2×3+2=8, 3×4+2=14, 4×5+2=22), so 5×6+2 gives 32.

abstract-reasoning-s09-q09

Each output is the letter's position in the alphabet, and Q is the 17th letter.

abstract-reasoning-s09-q10

The machine accepts numbers that read the same forwards and backwards, and only 45654 is such a palindrome.

abstract-reasoning-s10-q01

Reversing 58274 gives 47285, and deleting that result's last symbol leaves 4728.

abstract-reasoning-s10-q02

Trace the wrap-around jumps one at a time: 1 to 4, 4 to 7, 7 to 2, 2 to 5, and finally 5 to 8.

abstract-reasoning-s10-q03

Apply the alternating rules in order: 5 doubles to 10, minus 3 is 7, doubles to 14, minus 3 is 11.

abstract-reasoning-s10-q04

Shifting A, C, E forward two places gives C, E, G; reversing that intermediate result gives G, E, C.

abstract-reasoning-s10-q05

Each double flip cancels itself out, so only the three single flips matter: an odd number of flips turns white to black, whatever the order.

abstract-reasoning-s10-q06

Two quarter turns clockwise make a half turn, and a half turn points a left-facing arrow to the right.

abstract-reasoning-s10-q07

The gaps between terms double each step (+1, +2, +4, +8), so the next gap is +16, giving 34.

abstract-reasoning-s10-q08

The gaps grow by two each step (+4, +6, +8, +10), so the next gap is +12, giving 42.

abstract-reasoning-s10-q09

Handle each symbol type with its own rule: D and H step back to C and G, while 3 and 5 double to 6 and 10.

abstract-reasoning-s10-q10

Doubling AB gives AABB, and keeping the 1st and 3rd symbols of that result restores the original AB, the two operators undo each other.