Abstract reasoning: patterns, rules and transformations: open practice pack ########################################################################### 100 untimed questions across 10 authored sections. Pack: cognitive-skills-abstract-reasoning Source: cognitive-skills Pack version: v1 Worksheet items: 100 Authored hints: 0 Worked explanations: 100 ! 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. ! The answer key and worked explanations in this file belong only to this public, untimed educational practice source. No active aptitude suite or Novus Reasoning Challenge answer key is ever included in any download. 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? - A. Circle - B. Square - C. Triangle - D. Star Your answer: ______ 2. abstract-reasoning-s01-q02 ----------------------------- A shape repeats in three sizes: small, medium, large, small, medium. What comes next? - A. Small - B. Medium - C. Large - D. Extra large Your answer: ______ 3. abstract-reasoning-s01-q03 ----------------------------- A letter sequence runs: A, C, E, G. Which letter comes next? - A. I - B. H - C. J - D. K Your answer: ______ 4. abstract-reasoning-s01-q04 ----------------------------- A star pattern grows: ★, ★★, ★★★. Which group comes next? - A. ★ - B. ★★ - C. ★★★ - D. ★★★★ Your answer: ______ 5. abstract-reasoning-s01-q05 ----------------------------- An arrow turns through the sequence: up, right, down, left, up, right. Which direction comes next? - A. Up - B. Down - C. Left - D. Right Your answer: ______ 6. abstract-reasoning-s01-q06 ----------------------------- A dot pattern runs: ●, ●, ○, ●, ●, ○, ●, ●. What comes next? - A. ○ - B. ● - C. ●● - D. ○○ Your answer: ______ 7. abstract-reasoning-s01-q07 ----------------------------- A letter sequence runs backwards through the alphabet: Z, X, V, T. Which letter comes next? - A. S - B. Q - C. R - D. P Your answer: ______ 8. abstract-reasoning-s01-q08 ----------------------------- A symbol sequence runs: moon, star, sun, moon, star, sun, moon, star. What comes next? - A. Moon - B. Star - C. Cloud - D. Sun Your answer: ______ 9. abstract-reasoning-s01-q09 ----------------------------- A shape sequence gains one side each step: triangle, square, pentagon. Which shape comes next? - A. Heptagon - B. Octagon - C. Hexagon - D. Circle Your 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? - A. 10 dots - B. 16 dots - C. 12 dots - D. 24 dots Your 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? - A. Square - B. Triangle - C. Rectangle - D. Circle Your answer: ______ 12. abstract-reasoning-s02-q02 ------------------------------ Which of these capital letters does not belong with the other three? - A. S - B. X - C. K - D. T Your answer: ______ 13. abstract-reasoning-s02-q03 ------------------------------ Which of these capital letters does not belong with the other three? - A. A - B. H - C. F - D. M Your answer: ______ 14. abstract-reasoning-s02-q04 ------------------------------ Which of these does not belong with the other three? - A. Cube - B. Square - C. Sphere - D. Cylinder Your answer: ______ 15. abstract-reasoning-s02-q05 ------------------------------ Which of these letter pairs does not belong with the other three? - A. AB - B. XX - C. AA - D. MM Your answer: ______ 16. abstract-reasoning-s02-q06 ------------------------------ Which of these codes does not belong with the other three? - A. A1 - B. B2 - C. C3 - D. 4D Your answer: ______ 17. abstract-reasoning-s02-q07 ------------------------------ Which of these shapes does not belong with the other three? - A. Triangle - B. Hexagon - C. Pentagon - D. Heptagon Your answer: ______ 18. abstract-reasoning-s02-q08 ------------------------------ Which of these letters does not belong with the other three? - A. B - B. D - C. K - D. H Your answer: ______ 19. abstract-reasoning-s02-q09 ------------------------------ Which of these symbol groups does not belong with the other three? - A. ★★ - B. ▲▲▲ - C. ●●● - D. ■■■ Your answer: ______ 20. abstract-reasoning-s02-q10 ------------------------------ Which of these capital letters does not belong with the other three? - A. S - B. N - C. E - D. Z Your 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? - A. Red square - B. Green circle - C. Green square - D. Blue square Your answer: ______ 22. abstract-reasoning-s03-q02 ------------------------------ An arrow cycles: up, right, down, up, right, down, up. Which direction comes next? - A. Up - B. Right - C. Down - D. Left Your 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? - A. 3 - B. 6 - C. 9 - D. 12 Your answer: ______ 24. abstract-reasoning-s03-q04 ------------------------------ A letter sequence runs: A, B, A, C, A, D, A. Which letter comes next? - A. E - B. A - C. F - D. B Your 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? - A. White ▼ - B. Black ▲ - C. Black ▼ - D. White ▲ Your answer: ______ 26. abstract-reasoning-s03-q06 ------------------------------ The four suits repeat in a fixed order: ♠, ♥, ♦, ♣, ♠, ♥, ♦, ♣, and so on. Which symbol is 10th in the sequence? - A. ♠ - B. ♥ - C. ♦ - D. ♣ Your answer: ______ 27. abstract-reasoning-s03-q07 ------------------------------ The numbers 1, 2, 3 repeat forever: 1, 2, 3, 1, 2, 3, … What is the 12th term? - A. 3 - B. 1 - C. 2 - D. It cannot be determined Your answer: ______ 28. abstract-reasoning-s03-q08 ------------------------------ A pattern runs: ●, ■, ●●, ■■, ●●●. What comes next? - A. ●●●● - B. ■■ - C. ●●● - D. ■■■ Your answer: ______ 29. abstract-reasoning-s03-q09 ------------------------------ A pendulum pattern runs: left, centre, right, centre, left, centre, right. What comes next? - A. Left - B. Right - C. It cannot be determined - D. Centre Your 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? - A. Y - B. y - C. z - D. x Your 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? - A. 9 - B. 8 - C. 10 - D. 11 Your answer: ______ 32. abstract-reasoning-s04-q02 ------------------------------ A block pattern shrinks: 10 blocks, 8 blocks, 6 blocks, 4 blocks. How many blocks come next? - A. 3 - B. 0 - C. 1 - D. 2 Your answer: ______ 33. abstract-reasoning-s04-q03 ------------------------------ A tile pattern grows: 1, 2, 4, 7, 11. How many tiles come next? - A. 15 - B. 16 - C. 14 - D. 18 Your answer: ______ 34. abstract-reasoning-s04-q04 ------------------------------ A cell pattern doubles: 2, 4, 8, 16. How many cells come next? - A. 24 - B. 20 - C. 32 - D. 30 Your answer: ______ 35. abstract-reasoning-s04-q05 ------------------------------ A dot pattern halves: 64, 32, 16, 8. How many dots come next? - A. 6 - B. 2 - C. 0 - D. 4 Your answer: ______ 36. abstract-reasoning-s04-q06 ------------------------------ A counter pattern runs: 3, 6, 5, 10, 9, 18. What comes next? - A. 17 - B. 36 - C. 19 - D. 20 Your 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? - A. 20 - B. 24 - C. 25 - D. 36 Your 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? - A. 14 - B. 15 - C. 16 - D. 20 Your answer: ______ 39. abstract-reasoning-s04-q09 ------------------------------ A pattern rises and falls: 5, 8, 6, 9, 7, 10. What comes next? - A. 11 - B. 9 - C. 12 - D. 8 Your 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? - A. 13 - B. 12 - C. 16 - D. 11 Your 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? - A. Large circle - B. Large square - C. Small triangle - D. Large triangle Your 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.) - A. q - B. g - C. b - D. o Your answer: ______ 43. abstract-reasoning-s05-q03 ------------------------------ 3 is to triangle as 6 is to what? - A. Pentagon - B. Octagon - C. Heptagon - D. Hexagon Your answer: ______ 44. abstract-reasoning-s05-q04 ------------------------------ Black square is to white square as black circle is to what? - A. White square - B. Black triangle - C. White circle - D. Grey circle Your answer: ______ 45. abstract-reasoning-s05-q05 ------------------------------ AB is to BA as CD is to what? - A. CD - B. DC - C. CC - D. DD Your answer: ______ 46. abstract-reasoning-s05-q06 ------------------------------ Circle is to sphere as square is to what? - A. Cylinder - B. Pyramid - C. Cone - D. Cube Your answer: ______ 47. abstract-reasoning-s05-q07 ------------------------------ 3 is to 6 as 5 is to what? - A. 10 - B. 15 - C. 25 - D. 8 Your answer: ______ 48. abstract-reasoning-s05-q08 ------------------------------ A is to C as M is to what? - A. N - B. P - C. O - D. Q Your answer: ______ 49. abstract-reasoning-s05-q09 ------------------------------ XOX is to OXO as ABA is to what? - A. ABA - B. AAB - C. BAB - D. BBA Your answer: ______ 50. abstract-reasoning-s05-q10 ------------------------------ ▲▲● is to ●▲▲ as ■■★ is to what? - A. ■★■ - B. ■■★ - C. ★★■ - D. ★■■ Your 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 → ? - A. KML - B. LKM - C. MLK - D. MKL Your answer: ______ 52. abstract-reasoning-s06-q02 ------------------------------ The operator ◇ swaps only the first and last symbols of a string. What is ◇ applied to 2589? - A. 9852 - B. 5289 - C. 8529 - D. 9582 Your answer: ______ 53. abstract-reasoning-s06-q03 ------------------------------ The operator # doubles every symbol: #(AB) = AABB. What is #(XY)? - A. XXYY - B. XYXY - C. XY - D. YYXX Your answer: ______ 54. abstract-reasoning-s06-q04 ------------------------------ The operator ∆ removes every second symbol: ∆(ABCDE) = ACE. What is ∆(PQRST)? - A. QS - B. PRT - C. PQR - D. QST Your 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. - A. D, G, L - B. B, E, J - C. D, G, K - D. E, H, M Your answer: ______ 56. abstract-reasoning-s06-q06 ------------------------------ The operator ◇ swaps the first and last symbols; the operator # doubles every symbol. What is #(◇(ABC))? - A. AABBCC - B. CBACBA - C. CCBBAA - D. AACCBB Your answer: ______ 57. abstract-reasoning-s06-q07 ------------------------------ The operator ★ rotates a string one position left: ★(ABCD) = BCDA. What is ★(★(WXYZ))? - A. XYZW - B. ZWXY - C. WXYZ - D. YZWX Your 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? - A. □ - B. △ - C. ○ - D. ◇ Your answer: ______ 59. abstract-reasoning-s06-q09 ------------------------------ The operator ! reverses a string; the operator @ removes the first symbol. What is @(!(1234))? - A. 432 - B. 321 - C. 234 - D. 123 Your answer: ______ 60. abstract-reasoning-s06-q10 ------------------------------ The operator M appends a string's reverse to itself: M(AB) = ABBA. What is M(XY)? - A. XYYX - B. YXXY - C. XXYY - D. XYXY Your 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? - A. Square - B. Triangle - C. Star - D. Circle Your 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? - A. 4 - B. 5 - C. 6 - D. 7 Your 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? - A. Black - B. White - C. Grey - D. It cannot be determined Your 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? - A. A cross (both lines together) - B. A vertical line only - C. A horizontal line only - D. An empty cell Your 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? - A. Column 2 - B. Column 3 - C. Any column - D. Column 1 Your 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? - A. Octagon - B. Hexagon - C. Heptagon - D. Nonagon Your 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? - A. Right - B. Up - C. Down - D. Left Your 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)? - A. 9 - B. 6 - C. 8 - D. 12 Your 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? - A. A square only - B. A circle and a triangle - C. A circle, a square and a triangle - D. A square and a triangle Your 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? - A. Small - B. Large - C. Medium - D. It cannot be determined Your 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? - A. 40 - B. 5 - C. 35 - D. 50 Your answer: ______ 72. abstract-reasoning-s08-q02 ------------------------------ A sequence runs: A, Z, B, Y, C, X. What comes next? - A. W - B. E - C. D - D. Y Your answer: ______ 73. abstract-reasoning-s08-q03 ------------------------------ A sequence runs: ▲, A, ▲▲, B, ▲▲▲, C. What comes next? - A. D - B. ▲▲▲▲ - C. ▲▲▲ - D. ▲▲▲▲▲ Your answer: ______ 74. abstract-reasoning-s08-q04 ------------------------------ A sequence runs: 2, 3, 4, 6, 6, 9, 8. What comes next? - A. 10 - B. 9 - C. 11 - D. 12 Your answer: ______ 75. abstract-reasoning-s08-q05 ------------------------------ A sequence runs: Z, 1, X, 2, V, 4, T, 8. What comes next? - A. S - B. P - C. R - D. Q Your answer: ______ 76. abstract-reasoning-s08-q06 ------------------------------ A sequence runs: ●, ■■, ●●●, ■■■■, ●●●●●. What comes next? - A. ■■■■■■ - B. ●●●●●● - C. ■■■■■ - D. ●●●●●●● Your answer: ______ 77. abstract-reasoning-s08-q07 ------------------------------ A sequence runs: 1, 2, 4, 3, 9, 4, 16, 5. What comes next? - A. 20 - B. 6 - C. 36 - D. 25 Your answer: ______ 78. abstract-reasoning-s08-q08 ------------------------------ A sequence of codes runs: A1, C3, E5, G7. What comes next? - A. H8 - B. I9 - C. J9 - D. I8 Your answer: ______ 79. abstract-reasoning-s08-q09 ------------------------------ A sequence runs: 1, A, ●, 2, B, ●●, 3, C. What comes next? - A. 4 - B. D - C. ●● - D. ●●● Your answer: ______ 80. abstract-reasoning-s08-q10 ------------------------------ A sequence runs: 100, 1, 90, 2, 80, 4, 70, 8. What comes next? - A. 60 - B. 16 - C. 50 - D. 10 Your 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? - A. 40 - B. 93 - C. 36 - D. 39 Your answer: ______ 82. abstract-reasoning-s09-q02 ------------------------------ A machine transforms: ABC into BCD, and HIJ into IJK. What does it turn PQR into? - A. OPQ - B. PQS - C. RST - D. QRS Your 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? - A. 28 - B. 27 - C. 30 - D. 25 Your answer: ______ 84. abstract-reasoning-s09-q04 ------------------------------ A machine transforms: AB into ABB, and CD into CDD. What does it turn XY into? - A. XXY - B. XYXY - C. XYY - D. XY Your 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? - A. 12 - B. 35 - C. 13 - D. 11 Your answer: ______ 86. abstract-reasoning-s09-q06 ------------------------------ A machine transforms: ●●●● into ●●, and ●●●●●● into ●●●. What does it turn ●●●●●●●● into? - A. ●● - B. ●●●● - C. ●●●●● - D. ●●●●●● Your 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? - A. Octagon - B. Pentagon - C. Hexagon - D. Heptagon Your 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? - A. 30 - B. 28 - C. 34 - D. 32 Your 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? - A. 16 - B. 18 - C. 17 - D. 15 Your 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? - A. 45653 - B. 45664 - C. 45674 - D. 45654 Your 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))? - A. 8274 - B. 5827 - C. 4728 - D. 47285 Your 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? - A. Position 8 - B. Position 7 - C. Position 1 - D. Position 5 Your 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? - A. 14 - B. 17 - C. 7 - D. 11 Your 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? - A. CEG - B. GEC - C. ECA - D. ACG Your 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? - A. White - B. It depends on the order of the gates - C. It cannot be determined - D. Black Your 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? - A. Up - B. Right - C. Down - D. Left Your answer: ______ 97. abstract-reasoning-s10-q07 ------------------------------ A sequence runs: 3, 4, 6, 10, 18. What comes next? - A. 34 - B. 26 - C. 30 - D. 36 Your answer: ______ 98. abstract-reasoning-s10-q08 ------------------------------ A sequence runs: 2, 6, 12, 20, 30. What comes next? - A. 40 - B. 36 - C. 42 - D. 44 Your 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? - A. C6G10 - B. E6I10 - C. C6G1 - D. D6H10 Your answer: ______ 100. abstract-reasoning-s10-q10 ------------------------------- The operator # doubles every symbol (#(AB) = AABB); the operator ∆ removes every second symbol (∆(ABCD) = AC). What is ∆(#(AB))? - A. AABB - B. AB - C. BA - D. An empty string Your 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. No hint text was generated for them. Answer key ========== ! The answer key and worked explanations in this file belong only to this public, untimed educational practice source. No active aptitude suite or Novus Reasoning Challenge answer key is ever included in any download. Abstract reasoning: patterns, rules and transformations: open practice pack answer key Item Choice Answer -------------------------- ------ ----------------------------- abstract-reasoning-s01-q01 B Square abstract-reasoning-s01-q02 C Large abstract-reasoning-s01-q03 A I abstract-reasoning-s01-q04 D ★★★★ abstract-reasoning-s01-q05 B Down abstract-reasoning-s01-q06 A ○ abstract-reasoning-s01-q07 C R abstract-reasoning-s01-q08 D Sun abstract-reasoning-s01-q09 C Hexagon abstract-reasoning-s01-q10 B 16 dots abstract-reasoning-s02-q01 D Circle abstract-reasoning-s02-q02 A S abstract-reasoning-s02-q03 C F abstract-reasoning-s02-q04 B Square abstract-reasoning-s02-q05 A AB abstract-reasoning-s02-q06 D 4D abstract-reasoning-s02-q07 B Hexagon abstract-reasoning-s02-q08 C K abstract-reasoning-s02-q09 A ★★ abstract-reasoning-s02-q10 C E abstract-reasoning-s03-q01 C Green square abstract-reasoning-s03-q02 B Right abstract-reasoning-s03-q03 D 12 abstract-reasoning-s03-q04 A E abstract-reasoning-s03-q05 C Black ▼ abstract-reasoning-s03-q06 B ♥ abstract-reasoning-s03-q07 A 3 abstract-reasoning-s03-q08 D ■■■ abstract-reasoning-s03-q09 D Centre abstract-reasoning-s03-q10 B y abstract-reasoning-s04-q01 A 9 abstract-reasoning-s04-q02 D 2 abstract-reasoning-s04-q03 B 16 abstract-reasoning-s04-q04 C 32 abstract-reasoning-s04-q05 D 4 abstract-reasoning-s04-q06 A 17 abstract-reasoning-s04-q07 C 25 abstract-reasoning-s04-q08 B 15 abstract-reasoning-s04-q09 D 8 abstract-reasoning-s04-q10 A 13 abstract-reasoning-s05-q01 B Large square abstract-reasoning-s05-q02 A q abstract-reasoning-s05-q03 D Hexagon abstract-reasoning-s05-q04 C White circle abstract-reasoning-s05-q05 B DC abstract-reasoning-s05-q06 D Cube abstract-reasoning-s05-q07 A 10 abstract-reasoning-s05-q08 C O abstract-reasoning-s05-q09 C BAB abstract-reasoning-s05-q10 D ★■■ abstract-reasoning-s06-q01 C MLK abstract-reasoning-s06-q02 D 9582 abstract-reasoning-s06-q03 A XXYY abstract-reasoning-s06-q04 B PRT abstract-reasoning-s06-q05 A D, G, L abstract-reasoning-s06-q06 C CCBBAA abstract-reasoning-s06-q07 D YZWX abstract-reasoning-s06-q08 B △ abstract-reasoning-s06-q09 B 321 abstract-reasoning-s06-q10 A XYYX abstract-reasoning-s07-q01 D Circle abstract-reasoning-s07-q02 B 5 abstract-reasoning-s07-q03 C Grey abstract-reasoning-s07-q04 A A cross (both lines together) abstract-reasoning-s07-q05 D Column 1 abstract-reasoning-s07-q06 C Heptagon abstract-reasoning-s07-q07 B Up abstract-reasoning-s07-q08 A 9 abstract-reasoning-s07-q09 B A circle and a triangle abstract-reasoning-s07-q10 C Medium abstract-reasoning-s08-q01 A 40 abstract-reasoning-s08-q02 C D abstract-reasoning-s08-q03 B ▲▲▲▲ abstract-reasoning-s08-q04 D 12 abstract-reasoning-s08-q05 C R abstract-reasoning-s08-q06 A ■■■■■■ abstract-reasoning-s08-q07 D 25 abstract-reasoning-s08-q08 B I9 abstract-reasoning-s08-q09 D ●●● abstract-reasoning-s08-q10 A 60 abstract-reasoning-s09-q01 B 93 abstract-reasoning-s09-q02 D QRS abstract-reasoning-s09-q03 A 28 abstract-reasoning-s09-q04 C XYY abstract-reasoning-s09-q05 A 12 abstract-reasoning-s09-q06 B ●●●● abstract-reasoning-s09-q07 C Hexagon abstract-reasoning-s09-q08 D 32 abstract-reasoning-s09-q09 C 17 abstract-reasoning-s09-q10 D 45654 abstract-reasoning-s10-q01 C 4728 abstract-reasoning-s10-q02 A Position 8 abstract-reasoning-s10-q03 D 11 abstract-reasoning-s10-q04 B GEC abstract-reasoning-s10-q05 D Black abstract-reasoning-s10-q06 B Right abstract-reasoning-s10-q07 A 34 abstract-reasoning-s10-q08 C 42 abstract-reasoning-s10-q09 A C6G10 abstract-reasoning-s10-q10 B AB 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. Source: https://learn.novusstreamsolutions.com/cognitive-skills/abstract-reasoning