Inductive reasoning: patterns, rules, and generalisation: open practice pack ############################################################################ 100 untimed questions across 10 authored sections. Pack: cognitive-skills-inductive-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 ================= Ten untimed sections that build from simple sequences to judging the strength of generalisations. Work only from the information given in each prompt. Every item contains all the data you need. Choose one answer for each item. For a delayed-recall item, read its study text, cover it, and then answer without looking back. Number sequences: single-rule steps ----------------------------------- Find the one rule driving each sequence, then choose the next term. 1. inductive-reasoning-s01-q01 ------------------------------ What is the next number in the sequence 2, 4, 6, 8, ...? - A. 9 - B. 10 - C. 12 - D. 14 Your answer: ______ 2. inductive-reasoning-s01-q02 ------------------------------ What is the next number in the sequence 5, 10, 15, 20, ...? - A. 21 - B. 24 - C. 25 - D. 30 Your answer: ______ 3. inductive-reasoning-s01-q03 ------------------------------ What is the next number in the sequence 3, 6, 12, 24, ...? - A. 30 - B. 36 - C. 42 - D. 48 Your answer: ______ 4. inductive-reasoning-s01-q04 ------------------------------ What is the next number in the sequence 20, 17, 14, 11, ...? - A. 8 - B. 9 - C. 7 - D. 6 Your answer: ______ 5. inductive-reasoning-s01-q05 ------------------------------ What is the next number in the sequence 1, 4, 9, 16, ...? - A. 25 - B. 20 - C. 24 - D. 36 Your answer: ______ 6. inductive-reasoning-s01-q06 ------------------------------ What is the next number in the sequence 2, 5, 8, 11, ...? - A. 12 - B. 13 - C. 14 - D. 15 Your answer: ______ 7. inductive-reasoning-s01-q07 ------------------------------ What is the next number in the sequence 64, 32, 16, 8, ...? - A. 2 - B. 4 - C. 6 - D. 0 Your answer: ______ 8. inductive-reasoning-s01-q08 ------------------------------ What is the next number in the sequence 1, 2, 4, 7, 11, ...? - A. 13 - B. 14 - C. 15 - D. 16 Your answer: ______ 9. inductive-reasoning-s01-q09 ------------------------------ What is the next number in the sequence 90, 80, 71, 63, ...? - A. 56 - B. 55 - C. 57 - D. 54 Your answer: ______ 10. inductive-reasoning-s01-q10 ------------------------------- What is the next number in the sequence 7, 14, 21, 28, ...? - A. 32 - B. 35 - C. 36 - D. 42 Your answer: ______ Letter patterns and alphabet rules ---------------------------------- Treat the alphabet as a numbered line and work out the rule linking the letters. 11. inductive-reasoning-s02-q01 ------------------------------- What is the next letter in the sequence A, C, E, G, ...? - A. H - B. J - C. I - D. K Your answer: ______ 12. inductive-reasoning-s02-q02 ------------------------------- What is the next letter in the sequence Z, X, V, T, ...? - A. R - B. S - C. Q - D. P Your answer: ______ 13. inductive-reasoning-s02-q03 ------------------------------- What is the next letter in the sequence B, E, H, K, ...? - A. M - B. N - C. O - D. L Your answer: ______ 14. inductive-reasoning-s02-q04 ------------------------------- What is the next pair in the sequence AZ, BY, CX, DW, ...? - A. EW - B. FV - C. EU - D. EV Your answer: ______ 15. inductive-reasoning-s02-q05 ------------------------------- What is the next letter in the sequence A, B, D, G, K, ...? - A. N - B. O - C. P - D. Q Your answer: ______ 16. inductive-reasoning-s02-q06 ------------------------------- What is the next pair in the sequence CD, FG, IJ, LM, ...? - A. NO - B. OP - C. PQ - D. MN Your answer: ______ 17. inductive-reasoning-s02-q07 ------------------------------- What is the next letter in the sequence A, C, B, D, C, E, D, ...? - A. F - B. E - C. G - D. C Your answer: ______ 18. inductive-reasoning-s02-q08 ------------------------------- What is the next letter in the sequence M, N, L, O, K, P, ...? - A. I - B. Q - C. J - D. H Your answer: ______ 19. inductive-reasoning-s02-q09 ------------------------------- What comes next in the sequence A1, C3, E5, G7, ...? - A. H8 - B. J9 - C. I8 - D. I9 Your answer: ______ 20. inductive-reasoning-s02-q10 ------------------------------- Four of these letter pairs follow one rule and one breaks it: BD, EG, HJ, KN, PR. Which pair breaks the rule? - A. EG - B. KN - C. HJ - D. PR Your answer: ______ Shape and symbol patterns ------------------------- Each pattern uses described shapes or symbols: infer the repeating or evolving rule. 21. inductive-reasoning-s03-q01 ------------------------------- A pattern repeats: circle, square, triangle, circle, square, ... What shape comes next? - A. Circle - B. Square - C. Star - D. Triangle Your answer: ______ 22. inductive-reasoning-s03-q02 ------------------------------- Symbol sequence: ★ ★ ● ★ ★ ● ★ ... What is the eighth symbol? - A. ★ - B. ● - C. ■ - D. It cannot be determined Your answer: ______ 23. inductive-reasoning-s03-q03 ------------------------------- An arrow points up, then right, then down, then left, then up, then right. Where does it point next? - A. Left - B. Up - C. Down - D. Right Your answer: ______ 24. inductive-reasoning-s03-q04 ------------------------------- A row of cards shows 1 dot, then 3 dots, then 5 dots, then 7 dots. How many dots are on the next card? - A. 8 - B. 9 - C. 10 - D. 11 Your answer: ______ 25. inductive-reasoning-s03-q05 ------------------------------- A pattern alternates: large white square, small black square, large white square, small black square, large white square, ... What comes next? - A. Small black square - B. Large white square - C. Large black square - D. Small white square Your answer: ______ 26. inductive-reasoning-s03-q06 ------------------------------- A series of figures shows a triangle (3 sides), a square (4 sides), a pentagon (5 sides), then a hexagon (6 sides). Which figure comes next? - A. An octagon (8 sides) - B. A pentagon (5 sides) - C. A nonagon (9 sides) - D. A heptagon (7 sides) Your answer: ______ 27. inductive-reasoning-s03-q07 ------------------------------- Symbol groups appear in this order: ○ then ○● then ○●● then ○●●●. What is the next group? - A. ●●●●○ - B. ○●●● - C. ○●●●● - D. ●○●● Your answer: ______ 28. inductive-reasoning-s03-q08 ------------------------------- A square tile is shaded one quarter at a time: first the top-left quarter, then the top-right, then the bottom-right. Which quarter is shaded next? - A. Bottom-left - B. Top-left - C. Bottom-right - D. Top-right Your answer: ______ 29. inductive-reasoning-s03-q09 ------------------------------- A series of cards shows: 1 triangle, 2 squares, 3 triangles, 4 squares. What does the next card show? - A. 5 squares - B. 5 triangles - C. 4 triangles - D. 6 squares Your answer: ______ 30. inductive-reasoning-s03-q10 ------------------------------- Four tiles follow one rule and one breaks it: a triangle with 3 dots, a square with 4 dots, a pentagon with 5 dots, and a hexagon with 7 dots. Which tile breaks the rule? - A. The triangle with 3 dots - B. The square with 4 dots - C. The pentagon with 5 dots - D. The hexagon with 7 dots Your answer: ______ Classification: find the odd one out ------------------------------------ Work out the rule the group shares, then choose the item that does not obey it. 31. inductive-reasoning-s04-q01 ------------------------------- Which number does not belong with the others: 8, 64, 100, 216? - A. 8 - B. 64 - C. 100 - D. 216 Your answer: ______ 32. inductive-reasoning-s04-q02 ------------------------------- Which word does not belong with the others: letter, coffee, dinner, orange? - A. letter - B. coffee - C. dinner - D. orange Your answer: ______ 33. inductive-reasoning-s04-q03 ------------------------------- Which number does not belong with the others: 27, 35, 45, 63? - A. 27 - B. 35 - C. 45 - D. 63 Your answer: ______ 34. inductive-reasoning-s04-q04 ------------------------------- Which letter group does not belong with the others: NPS, BDF, HJL, PRT? - A. NPS - B. BDF - C. HJL - D. PRT Your answer: ______ 35. inductive-reasoning-s04-q05 ------------------------------- Which pair does not belong with the others: (3, 7), (6, 4), (5, 6), (8, 2)? - A. (3, 7) - B. (6, 4) - C. (5, 6) - D. (8, 2) Your answer: ______ 36. inductive-reasoning-s04-q06 ------------------------------- Which word does not belong with the others: level, civic, rotor, tiles? - A. level - B. civic - C. rotor - D. tiles Your answer: ______ 37. inductive-reasoning-s04-q07 ------------------------------- Which number does not belong with the others: 46, 53, 64, 82? - A. 46 - B. 53 - C. 64 - D. 82 Your answer: ______ 38. inductive-reasoning-s04-q08 ------------------------------- Which triple does not belong with the others: (3, 6, 12), (5, 10, 20), (4, 8, 12), (7, 14, 28)? - A. (3, 6, 12) - B. (5, 10, 20) - C. (4, 8, 12) - D. (7, 14, 28) Your answer: ______ 39. inductive-reasoning-s04-q09 ------------------------------- Which clock time does not belong with the others: 14:14, 12:21, 15:51, 10:01? - A. 14:14 - B. 12:21 - C. 15:51 - D. 10:01 Your answer: ______ 40. inductive-reasoning-s04-q10 ------------------------------- Which group does not belong with the others: (2, 3, 5), (5, 7, 12), (11, 13, 24), (7, 11, 17)? - A. (2, 3, 5) - B. (5, 7, 12) - C. (11, 13, 24) - D. (7, 11, 17) Your answer: ______ Analogies: transfer the relation -------------------------------- Work out the relation in the example pair, then apply exactly the same relation to the new case. 41. inductive-reasoning-s05-q01 ------------------------------- 3 is to 6 as 7 is to ...? - A. 14 - B. 10 - C. 21 - D. 17 Your answer: ______ 42. inductive-reasoning-s05-q02 ------------------------------- C is to F as J is to ...? - A. L - B. M - C. N - D. K Your answer: ______ 43. inductive-reasoning-s05-q03 ------------------------------- “stop” is to “pots” as “flow” is to ...? - A. fowl - B. low - C. wolf - D. flew Your answer: ______ 44. inductive-reasoning-s05-q04 ------------------------------- 4 is to 16, and 5 is to 25. Following the same rule, 7 is to ...? - A. 28 - B. 35 - C. 14 - D. 49 Your answer: ______ 45. inductive-reasoning-s05-q05 ------------------------------- 25 is to 5 as 64 is to ...? - A. 6 - B. 8 - C. 32 - D. 16 Your answer: ______ 46. inductive-reasoning-s05-q06 ------------------------------- BC is to EF as JK is to ...? - A. MN - B. NO - C. LM - D. KL Your answer: ______ 47. inductive-reasoning-s05-q07 ------------------------------- 1/2 is to 2 as 1/8 is to ...? - A. 4 - B. 16 - C. 1/4 - D. 8 Your answer: ______ 48. inductive-reasoning-s05-q08 ------------------------------- The pair (3, 5) is to 8 as the pair (7, 6) is to ...? - A. 12 - B. 13 - C. 42 - D. 1 Your answer: ______ 49. inductive-reasoning-s05-q09 ------------------------------- A triangle is to 3 as a hexagon is to ...? - A. 6 - B. 5 - C. 8 - D. 4 Your answer: ______ 50. inductive-reasoning-s05-q10 ------------------------------- In a letter code, CAT is written as DBU. Using the same code, how is DOG written? - A. EOH - B. CPF - C. EPH - D. DPH Your answer: ______ Alternating and interleaved sequences ------------------------------------- These sequences mix two rules at once: separate the strands before predicting the next term. 51. inductive-reasoning-s06-q01 ------------------------------- What is the next number in the sequence 1, 10, 2, 20, 3, 30, 4, ...? - A. 5 - B. 40 - C. 31 - D. 50 Your answer: ______ 52. inductive-reasoning-s06-q02 ------------------------------- What is the next number in the sequence 2, 100, 4, 90, 6, 80, ...? - A. 70 - B. 10 - C. 8 - D. 9 Your answer: ______ 53. inductive-reasoning-s06-q03 ------------------------------- What is the next number in the sequence 5, 6, 8, 9, 11, 12, ...? - A. 13 - B. 15 - C. 16 - D. 14 Your answer: ______ 54. inductive-reasoning-s06-q04 ------------------------------- What comes next in the sequence A, 2, C, 4, E, 6, ...? - A. G - B. 8 - C. F - D. 7 Your answer: ______ 55. inductive-reasoning-s06-q05 ------------------------------- What is the next number in the sequence 40, 1, 35, 3, 30, 9, 25, ...? - A. 20 - B. 18 - C. 27 - D. 81 Your answer: ______ 56. inductive-reasoning-s06-q06 ------------------------------- What is the next number in the sequence 1, 1, 2, 3, 5, 8, ...? - A. 11 - B. 12 - C. 10 - D. 13 Your answer: ______ 57. inductive-reasoning-s06-q07 ------------------------------- What is the next number in the sequence 100, 2, 90, 4, 81, 8, 73, ...? - A. 66 - B. 16 - C. 12 - D. 64 Your answer: ______ 58. inductive-reasoning-s06-q08 ------------------------------- What comes next in the sequence J, 1, K, 3, M, 6, P, 10, ...? - A. Q - B. S - C. T - D. U Your answer: ______ 59. inductive-reasoning-s06-q09 ------------------------------- What is the next number in the sequence 6, 11, 8, 13, 10, 15, 12, ...? - A. 17 - B. 14 - C. 16 - D. 19 Your answer: ______ 60. inductive-reasoning-s06-q10 ------------------------------- What is the next number in the sequence 2, 6, 3, 9, 4.5, 13.5, ...? - A. 27 - B. 20.25 - C. 7 - D. 6.75 Your answer: ______ Generalising from observations ------------------------------ Read the observations and choose the conclusion they best support, using only what is given. 61. inductive-reasoning-s07-q01 ------------------------------- Ana has recorded 47 swan sightings at her local lake this year, and every swan she recorded was white. Which conclusion do her observations best support? - A. Swans at this lake are usually white. - B. All swans everywhere are white. - C. The next swan Ana sees cannot be a different colour. - D. White is the only possible swan colour. Your answer: ______ 62. inductive-reasoning-s07-q02 ------------------------------- A baker notices that rye loaf sales rose on each of the last six rainy Saturdays and fell on each of the last five sunny Saturdays. Which conclusion is best supported? - A. Rain causes people to crave rye bread. - B. Rye sales rise on rainy days in every town. - C. At this bakery, rainy Saturdays have been associated with higher rye sales. - D. Sunny weather stops people eating bread. Your answer: ______ 63. inductive-reasoning-s07-q03 ------------------------------- In a sample of 200 bolts from Machine A, 3 were faulty. In a sample of 200 bolts from Machine B, 21 were faulty. Which conclusion is best supported? - A. Machine B is broken and must be replaced. - B. Machine B's output showed a higher fault rate in these samples. - C. Machine A never produces faulty bolts. - D. The next bolt from Machine B will certainly be faulty. Your answer: ______ 64. inductive-reasoning-s07-q04 ------------------------------- In one garden bed, each of the 12 tomato plants given compost grew taller than each of the 12 plants without compost. Which is the safest reading of this result? - A. Compost makes all plants grow taller. - B. The gardener's soil must be unusually poor. - C. Tomatoes cannot grow well without compost. - D. In this garden's trial, compost went together with taller growth. Your answer: ______ 65. inductive-reasoning-s07-q05 ------------------------------- For five weekdays in a row, the 08:15 bus arrived between 8 and 10 minutes late, while the 08:45 arrived on time. What is the most reasonable expectation for tomorrow? - A. The 08:15 is likely, though not certain, to be late again. - B. The 08:15 will be exactly 9 minutes late. - C. The 08:45 can never run late. - D. Every bus in the city is unreliable. Your answer: ______ 66. inductive-reasoning-s07-q06 ------------------------------- A café surveyed 60 customers and found one in four chose oat milk, but the survey ran only on weekday mornings. Before generalising to all customers, which caution matters most? - A. Sixty people can never tell you anything useful. - B. Oat milk drinkers probably avoid surveys. - C. The sample may not represent afternoon or weekend customers. - D. The survey should have asked about tea instead. Your answer: ______ 67. inductive-reasoning-s07-q07 ------------------------------- A student notices she scored higher on every quiz taken after at least eight hours' sleep than on any quiz taken after less. Which conclusion is best supported? - A. For this student, more sleep has gone together with higher quiz scores. - B. Sleep causes high marks for all students. - C. She is guaranteed a top mark if she sleeps eight hours tonight. - D. Quizzes taken while tired are unfairly difficult. Your answer: ______ 68. inductive-reasoning-s07-q08 ------------------------------- A bag of counters is sampled 300 times (with the counter returned each time): red came out 148 times and blue 152 times. Which inference is most reasonable? - A. The bag holds exactly 150 red and 150 blue counters. - B. The bag likely holds red and blue in roughly equal numbers. - C. The next draw must be red to balance the counts. - D. Blue counters are heavier than red ones. Your answer: ______ 69. inductive-reasoning-s07-q09 ------------------------------- Across four separate climbs, a hiker recorded a temperature drop of about 1°C for every 150 metres of ascent. What should she expect for a 600-metre climb? - A. A drop of exactly 4.0°C, guaranteed. - B. A drop of about 2°C. - C. A drop of roughly 4°C. - D. No prediction is possible from her records. Your answer: ______ 70. inductive-reasoning-s07-q10 ------------------------------- A library's logs show late returns happen most often for books borrowed on Fridays. The logs also show most books are borrowed on Fridays. Which point most weakens the rule 'Friday borrowing causes lateness'? - A. Some late books were borrowed on Mondays. - B. The library is closed on Sundays. - C. Lateness is measured in whole days. - D. Fridays supply most borrowings overall, so they would lead any count, including late returns, even with no special effect. Your answer: ______ Grid and matrix patterns ------------------------ Each grid follows row or column rules: recover them and fill the missing cell. 71. inductive-reasoning-s08-q01 ------------------------------- A 3×3 grid reads: row 1: 1, 2, 3; row 2: 4, 5, 6; row 3: 7, 8, ?. What number completes it? - A. 6 - B. 8 - C. 10 - D. 9 Your answer: ______ 72. inductive-reasoning-s08-q02 ------------------------------- A 3×3 grid reads: row 1: 2, 5, 7; row 2: 3, 6, 9; row 3: 4, 7, ?. What number completes it? - A. 10 - B. 11 - C. 12 - D. 28 Your answer: ______ 73. inductive-reasoning-s08-q03 ------------------------------- A 3×3 grid reads: row 1: 2, 3, 5; row 2: 4, 6, 10; row 3: 8, 12, ?. What number completes it? - A. 20 - B. 15 - C. 24 - D. 18 Your answer: ______ 74. inductive-reasoning-s08-q04 ------------------------------- A 3×3 grid reads: row 1: 2, 3, 6; row 2: 4, 2, 8; row 3: 3, 5, ?. What number completes it? - A. 8 - B. 12 - C. 15 - D. 35 Your answer: ______ 75. inductive-reasoning-s08-q05 ------------------------------- A 3×3 grid of shaded squares reads: row 1: white, grey, black; row 2: black, white, grey; row 3: grey, ?, white. What shade fills the missing cell? - A. White - B. Black - C. Grey - D. Any shade fits Your answer: ______ 76. inductive-reasoning-s08-q06 ------------------------------- A 3×3 grid reads: row 1: 4, 9, 2; row 2: 3, 5, 7; row 3: 8, 1, ?. What number completes it? - A. 5 - B. 7 - C. 4 - D. 6 Your answer: ______ 77. inductive-reasoning-s08-q07 ------------------------------- A 3×3 grid reads: row 1: 1, 2, 3; row 2: 2, 4, 7; row 3: 3, 7, ?. What number completes it? - A. 10 - B. 12 - C. 14 - D. 16 Your answer: ______ 78. inductive-reasoning-s08-q08 ------------------------------- A 3×3 grid of letters reads: row 1: A, D, G; row 2: B, E, H; row 3: C, F, ?. What letter completes it? - A. I - B. J - C. K - D. H Your answer: ______ 79. inductive-reasoning-s08-q09 ------------------------------- A 2×2 grid reads: top row: 6 then 3; bottom row: 10 then ?. What number completes it? - A. 7 - B. 5 - C. 20 - D. 8 Your answer: ______ 80. inductive-reasoning-s08-q10 ------------------------------- A 3×3 grid reads: row 1: 9, 4, 5; row 2: 12, 5, 7; row 3: 15, 6, ?. What number completes it? - A. 8 - B. 11 - C. 10 - D. 9 Your answer: ______ Rule discovery: function machines and codes ------------------------------------------- Infer the hidden rule that turns each input into its output, then apply it to the new case. 81. inductive-reasoning-s09-q01 ------------------------------- A machine turns 3 into 7, 5 into 11, and 8 into 17. What does it turn 10 into? - A. 21 - B. 20 - C. 19 - D. 25 Your answer: ______ 82. inductive-reasoning-s09-q02 ------------------------------- A machine turns 4 into 2, 10 into 5, and 16 into 8. What does it turn 26 into? - A. 24 - B. 52 - C. 12 - D. 13 Your answer: ______ 83. inductive-reasoning-s09-q03 ------------------------------- In a code, LAMP is written as MBNQ. Using the same code, how is GATE written? - A. FZSD - B. HBUF - C. HAUE - D. GBTF Your answer: ______ 84. inductive-reasoning-s09-q04 ------------------------------- A machine turns 2 into 3, 3 into 5, 5 into 9, and 6 into 11. What does it turn 9 into? - A. 15 - B. 16 - C. 17 - D. 18 Your answer: ______ 85. inductive-reasoning-s09-q05 ------------------------------- A code maps 1 to A, 4 to D, and 7 to G. What letter does the same code map 11 to? - A. K - B. J - C. L - D. I Your answer: ______ 86. inductive-reasoning-s09-q06 ------------------------------- A machine turns 5 into 30, 7 into 42, and 9 into 54. What does it turn 11 into? - A. 60 - B. 72 - C. 55 - D. 66 Your answer: ______ 87. inductive-reasoning-s09-q07 ------------------------------- A code turns NET into TEN, RAW into WAR, and PIN into NIP. What does it turn BUS into? - A. USB - B. BSU - C. SUB - D. SBU Your answer: ______ 88. inductive-reasoning-s09-q08 ------------------------------- A machine turns 2 into 8, 3 into 27, and 4 into 64. What does it turn 5 into? - A. 100 - B. 125 - C. 75 - D. 625 Your answer: ______ 89. inductive-reasoning-s09-q09 ------------------------------- A machine turns 3 into 10, 6 into 19, and 10 into 31. What does it turn 12 into? - A. 37 - B. 36 - C. 41 - D. 34 Your answer: ______ 90. inductive-reasoning-s09-q10 ------------------------------- A machine turns 23 into 5, 47 into 11, 65 into 11, and 81 into 9. What does it turn 76 into? - A. 6 - B. 11 - C. 76 - D. 13 Your answer: ______ Extended extrapolation and inductive strength --------------------------------------------- These items combine several inductive steps: extrapolate carefully and judge how strong each inference really is. 91. inductive-reasoning-s10-q01 ------------------------------- What is the next number in the sequence 4, 6, 10, 18, 34, ...? - A. 62 - B. 66 - C. 68 - D. 70 Your answer: ______ 92. inductive-reasoning-s10-q02 ------------------------------- What is the next number in the sequence 2, 6, 12, 20, 30, ...? - A. 40 - B. 36 - C. 42 - D. 44 Your answer: ______ 93. inductive-reasoning-s10-q03 ------------------------------- Which of these generalisations rests on the strongest inductive evidence? - A. A random sample of 1,000 households across a city found 90% recycle weekly, so most households in that city recycle weekly. - B. Three neighbours on one street recycle, so the whole country recycles. - C. One street's recycling bins were full on Monday, so everyone recycles. - D. A recycling firm's advert says most people recycle, so most people do. Your answer: ______ 94. inductive-reasoning-s10-q04 ------------------------------- A seedling grew 2 cm in week one, 4 cm in week two, and 8 cm in week three. Someone predicts it will grow 256 cm in week eight by continuing the doubling. What is the main inductive weakness of this prediction? - A. The arithmetic of the doubling is wrong. - B. Three weeks is an unusually large sample. - C. Growth cannot be measured in centimetres. - D. It assumes a short-run pattern will continue indefinitely without limit. Your answer: ______ 95. inductive-reasoning-s10-q05 ------------------------------- A sequence of pairs runs (1, 1), (2, 4), (3, 9), (4, 16), (?, 36). What is the missing first number? - A. 5 - B. 18 - C. 6 - D. 7 Your answer: ______ 96. inductive-reasoning-s10-q06 ------------------------------- What is the next number in the sequence 3, 4, 6, 8, 12, 14, 18, 20, ...? - A. 22 - B. 24 - C. 26 - D. 21 Your answer: ______ 97. inductive-reasoning-s10-q07 ------------------------------- Researchers have examined 40 beetles near a cave's entrance and all were blind. Which additional observation would most strengthen the generalisation 'all the beetles in this cave are blind'? - A. Re-examining the same 40 beetles a second time. - B. Reading that beetles in other caves are often blind. - C. Counting the legs of the beetles already collected. - D. Sampling beetles from deep, unexplored parts of the cave and finding them blind too. Your answer: ______ 98. inductive-reasoning-s10-q08 ------------------------------- What comes next in the sequence Z1, X2, V4, T8, ...? - A. R16 - B. S16 - C. R12 - D. Q16 Your answer: ______ 99. inductive-reasoning-s10-q09 ------------------------------- What is the next number in the sequence 1, 2, 6, 24, 120, ...? - A. 600 - B. 720 - C. 620 - D. 840 Your answer: ______ 100. inductive-reasoning-s10-q10 -------------------------------- A sequence runs 2, 4, 8, 14, 22. Which rule fits every step of the sequence? - A. Each term is double the previous term. - B. Each term adds 2 to the previous term. - C. The amount added grows by 2 each step. - D. Each term is its position number squared. 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. Inductive reasoning: patterns, rules, and generalisation: open practice pack answer key Item Choice Answer --------------------------- ------ --------------------------------------------------------------------------------------------------------------------------- inductive-reasoning-s01-q01 B 10 inductive-reasoning-s01-q02 C 25 inductive-reasoning-s01-q03 D 48 inductive-reasoning-s01-q04 A 8 inductive-reasoning-s01-q05 A 25 inductive-reasoning-s01-q06 C 14 inductive-reasoning-s01-q07 B 4 inductive-reasoning-s01-q08 D 16 inductive-reasoning-s01-q09 A 56 inductive-reasoning-s01-q10 B 35 inductive-reasoning-s02-q01 C I inductive-reasoning-s02-q02 A R inductive-reasoning-s02-q03 B N inductive-reasoning-s02-q04 D EV inductive-reasoning-s02-q05 C P inductive-reasoning-s02-q06 B OP inductive-reasoning-s02-q07 A F inductive-reasoning-s02-q08 C J inductive-reasoning-s02-q09 D I9 inductive-reasoning-s02-q10 B KN inductive-reasoning-s03-q01 D Triangle inductive-reasoning-s03-q02 A ★ inductive-reasoning-s03-q03 C Down inductive-reasoning-s03-q04 B 9 inductive-reasoning-s03-q05 A Small black square inductive-reasoning-s03-q06 D A heptagon (7 sides) inductive-reasoning-s03-q07 C ○●●●● inductive-reasoning-s03-q08 A Bottom-left inductive-reasoning-s03-q09 B 5 triangles inductive-reasoning-s03-q10 D The hexagon with 7 dots inductive-reasoning-s04-q01 C 100 inductive-reasoning-s04-q02 D orange inductive-reasoning-s04-q03 B 35 inductive-reasoning-s04-q04 A NPS inductive-reasoning-s04-q05 C (5, 6) inductive-reasoning-s04-q06 D tiles inductive-reasoning-s04-q07 B 53 inductive-reasoning-s04-q08 C (4, 8, 12) inductive-reasoning-s04-q09 A 14:14 inductive-reasoning-s04-q10 D (7, 11, 17) inductive-reasoning-s05-q01 A 14 inductive-reasoning-s05-q02 B M inductive-reasoning-s05-q03 C wolf inductive-reasoning-s05-q04 D 49 inductive-reasoning-s05-q05 B 8 inductive-reasoning-s05-q06 A MN inductive-reasoning-s05-q07 D 8 inductive-reasoning-s05-q08 B 13 inductive-reasoning-s05-q09 A 6 inductive-reasoning-s05-q10 C EPH inductive-reasoning-s06-q01 B 40 inductive-reasoning-s06-q02 C 8 inductive-reasoning-s06-q03 D 14 inductive-reasoning-s06-q04 A G inductive-reasoning-s06-q05 C 27 inductive-reasoning-s06-q06 D 13 inductive-reasoning-s06-q07 B 16 inductive-reasoning-s06-q08 C T inductive-reasoning-s06-q09 A 17 inductive-reasoning-s06-q10 D 6.75 inductive-reasoning-s07-q01 A Swans at this lake are usually white. inductive-reasoning-s07-q02 C At this bakery, rainy Saturdays have been associated with higher rye sales. inductive-reasoning-s07-q03 B Machine B's output showed a higher fault rate in these samples. inductive-reasoning-s07-q04 D In this garden's trial, compost went together with taller growth. inductive-reasoning-s07-q05 A The 08:15 is likely, though not certain, to be late again. inductive-reasoning-s07-q06 C The sample may not represent afternoon or weekend customers. inductive-reasoning-s07-q07 A For this student, more sleep has gone together with higher quiz scores. inductive-reasoning-s07-q08 B The bag likely holds red and blue in roughly equal numbers. inductive-reasoning-s07-q09 C A drop of roughly 4°C. inductive-reasoning-s07-q10 D Fridays supply most borrowings overall, so they would lead any count, including late returns, even with no special effect. inductive-reasoning-s08-q01 D 9 inductive-reasoning-s08-q02 B 11 inductive-reasoning-s08-q03 A 20 inductive-reasoning-s08-q04 C 15 inductive-reasoning-s08-q05 B Black inductive-reasoning-s08-q06 D 6 inductive-reasoning-s08-q07 C 14 inductive-reasoning-s08-q08 A I inductive-reasoning-s08-q09 B 5 inductive-reasoning-s08-q10 D 9 inductive-reasoning-s09-q01 A 21 inductive-reasoning-s09-q02 D 13 inductive-reasoning-s09-q03 B HBUF inductive-reasoning-s09-q04 C 17 inductive-reasoning-s09-q05 A K inductive-reasoning-s09-q06 D 66 inductive-reasoning-s09-q07 C SUB inductive-reasoning-s09-q08 B 125 inductive-reasoning-s09-q09 A 37 inductive-reasoning-s09-q10 D 13 inductive-reasoning-s10-q01 B 66 inductive-reasoning-s10-q02 C 42 inductive-reasoning-s10-q03 A A random sample of 1,000 households across a city found 90% recycle weekly, so most households in that city recycle weekly. inductive-reasoning-s10-q04 D It assumes a short-run pattern will continue indefinitely without limit. inductive-reasoning-s10-q05 C 6 inductive-reasoning-s10-q06 B 24 inductive-reasoning-s10-q07 D Sampling beetles from deep, unexplored parts of the cave and finding them blind too. inductive-reasoning-s10-q08 A R16 inductive-reasoning-s10-q09 B 720 inductive-reasoning-s10-q10 C The amount added grows by 2 each step. Worked explanations =================== inductive-reasoning-s01-q01 Each term rises by 2, so the sequence continues 8 + 2 = 10. inductive-reasoning-s01-q02 The sequence adds 5 at every step: 20 + 5 = 25. inductive-reasoning-s01-q03 Each term is double the one before, so the next term is 24 × 2 = 48. Checking the rule against every given term protects you from guessing off just the last pair. inductive-reasoning-s01-q04 The sequence falls by 3 each step: 11 − 3 = 8. inductive-reasoning-s01-q05 These are the square numbers 1², 2², 3², 4², the next is 5² = 25. When gaps keep widening, test whether the terms are squares or another named family. inductive-reasoning-s01-q06 Each term adds 3: 11 + 3 = 14. inductive-reasoning-s01-q07 Each term is half the one before: 8 ÷ 2 = 4. inductive-reasoning-s01-q08 The gaps grow by one each time (+1, +2, +3, +4), so the next gap is +5: 11 + 5 = 16. Writing out the differences is the quickest way to expose a hidden second-level rule. inductive-reasoning-s01-q09 The amount subtracted shrinks by one each step (−10, −9, −8), so the next step is −7: 63 − 7 = 56. inductive-reasoning-s01-q10 These are the multiples of 7 in order, so the next is 7 × 5 = 35. inductive-reasoning-s02-q01 The sequence skips one letter each step (two places forward), so after G comes I. inductive-reasoning-s02-q02 Each step moves two letters backwards through the alphabet: T back two is R. inductive-reasoning-s02-q03 Each letter sits three places after the previous one, and three past K is N. Converting letters to alphabet positions (2, 5, 8, 11) makes the +3 rule obvious. inductive-reasoning-s02-q04 The first letter walks forward from A while the second walks backwards from Z, so the pair after DW joins E with V. inductive-reasoning-s02-q05 The jump grows by one letter each time (+1, +2, +3, +4), so the next jump is five letters: K to P. inductive-reasoning-s02-q06 Each pair is two neighbouring letters, and each pair starts three letters after the last (C, F, I, L, O), giving O followed by P. inductive-reasoning-s02-q07 The steps alternate two forward, one back (A→C→B→D→C→E→D), so the next step is two forward: F. Alternating sequences reward tracking the pattern of moves, not just the letters. inductive-reasoning-s02-q08 The jumps alternate direction and grow by one: +1, −2, +3, −4, +5, so the next move is −6, taking P (position 16) to J (position 10). inductive-reasoning-s02-q09 The letters advance two at a time (A, C, E, G, I) and each number is that letter's alphabet position. The 9th letter is I, giving I9. inductive-reasoning-s02-q10 In every conforming pair the second letter comes exactly two after the first (B→D, E→G, H→J, P→R); K to N is a three-letter jump. inductive-reasoning-s03-q01 The three-shape unit circle–square–triangle repeats, and the second unit still needs its triangle. inductive-reasoning-s03-q02 The repeating unit is star, star, dot. The seventh symbol starts a new unit, so the second star comes next. inductive-reasoning-s03-q03 The arrow rotates a quarter turn clockwise each step, so after right it points down. inductive-reasoning-s03-q04 The dot count climbs through the odd numbers, adding two each time: 7 + 2 = 9. inductive-reasoning-s03-q05 Size and colour change together in a two-step cycle, so a large white square is always followed by a small black one. inductive-reasoning-s03-q06 The side count rises by one with each figure, so a seven-sided shape follows the hexagon. inductive-reasoning-s03-q07 Each group keeps its single white circle and gains one more black circle, so the next group has four black circles after the white one. inductive-reasoning-s03-q08 The shading moves one quarter clockwise each step, so after bottom-right it reaches bottom-left. inductive-reasoning-s03-q09 Two rules run together: the count rises by one each card while the shape alternates between triangle and square, so five triangles come next. inductive-reasoning-s03-q10 The shared rule is that the dot count equals the number of sides, so a six-sided hexagon should carry six dots, not seven. inductive-reasoning-s04-q01 8, 64, and 216 are perfect cubes (2³, 4³, 6³); 100 is a square but not a cube. inductive-reasoning-s04-q02 The first three each contain a doubled letter (tt, ff, nn); orange has no repeated adjacent letters. When the odd one out isn't about meaning, check the words' structure. inductive-reasoning-s04-q03 27, 45, and 63 are all multiples of 9; dividing 35 by 9 leaves a remainder. inductive-reasoning-s04-q04 In the other groups each letter steps forward two places (B–D–F, H–J–L, P–R–T); N–P–S ends with a three-letter jump. inductive-reasoning-s04-q05 Every other pair sums to 10; 5 + 6 makes 11. inductive-reasoning-s04-q06 Level, civic, and rotor read the same forwards and backwards (palindromes); tiles does not. inductive-reasoning-s04-q07 46, 64, and 82 each have digits that sum to ten; 5 + 3 gives only eight. Digit sums are a classic hidden property worth testing when face value shows no pattern. inductive-reasoning-s04-q08 In the other triples each number doubles the one before; 8 to 12 adds 4 instead of doubling. inductive-reasoning-s04-q09 Read as digit strings, 10:01, 12:21, and 15:51 are palindromes (1001, 1221, 1551); 1414 reversed gives 4141, so it breaks the rule. inductive-reasoning-s04-q10 In the conforming groups the third number is the sum of the first two (2+3=5, 5+7=12, 11+13=24); 7 + 11 is 18, not 17. inductive-reasoning-s05-q01 6 is double 3, so apply the same doubling: 7 × 2 = 14. inductive-reasoning-s05-q02 F sits three letters after C, and three letters after J is M. inductive-reasoning-s05-q03 The second word spells the first backwards, and flow reversed is wolf. Watch for near-misses that merely rearrange the same letters. inductive-reasoning-s05-q04 Both example pairs square the first number (4² = 16, 5² = 25), multiplying by 4 would fail the second pair, so 7² = 49. A second example exists precisely to rule out rival rules. inductive-reasoning-s05-q05 The second number is the square root of the first, and the square root of 64 is 8. inductive-reasoning-s05-q06 Each letter of the pair moves three places forward: J becomes M and K becomes N. inductive-reasoning-s05-q07 The second value is the reciprocal of the first, and the reciprocal of 1/8 is 8. inductive-reasoning-s05-q08 The single number is the sum of the pair: 7 + 6 = 13. inductive-reasoning-s05-q09 The number counts the shape's sides: a triangle has three and a hexagon has six. inductive-reasoning-s05-q10 Every letter shifts one place forward (C→D, A→B, T→U), so D→E, O→P, G→H. Decode the rule letter by letter rather than trusting the overall look of an option. inductive-reasoning-s06-q01 Two strands interleave (1, 2, 3, 4 and 10, 20, 30), and the next position belongs to the tens strand: 40. inductive-reasoning-s06-q02 Odd positions climb by two (2, 4, 6, 8) while even positions fall by ten; the seventh term continues the climbing strand. inductive-reasoning-s06-q03 The steps alternate +1, +2, +1, +2; after 12 the next step is +2, giving 14. inductive-reasoning-s06-q04 Letters skipping one place (A, C, E, G) alternate with even numbers, and the next position is a letter. inductive-reasoning-s06-q05 One strand falls by five (40, 35, 30, 25) while the other triples (1, 3, 9); the next term triples again: 9 × 3 = 27. inductive-reasoning-s06-q06 Each term is the sum of the two before it: 5 + 8 = 13. When neither differences nor ratios settle, try combining earlier terms. inductive-reasoning-s06-q07 The even positions double each time (2, 4, 8, 16), while the falling strand shrinks its step by one (−10, −9, −8); the next position belongs to the doubling strand. inductive-reasoning-s06-q08 The letter strand's jump grows by one each time (J→K is one, K→M two, M→P three), so the next letter is four past P: T. inductive-reasoning-s06-q09 Both interleaved strands rise by two (6, 8, 10, 12 and 11, 13, 15); the next term continues the second strand: 17. inductive-reasoning-s06-q10 The steps alternate multiply-by-three and halve (2×3=6, 6÷2=3, 3×3=9, 9÷2=4.5); after 13.5 comes halving: 6.75. inductive-reasoning-s07-q01 Induction supports a probable, local generalisation: many consistent sightings at one lake. Claims about all swans, or about what cannot happen, outrun the evidence. inductive-reasoning-s07-q02 Repeated pairing of rain and higher sales supports an association at this bakery; claiming a cause, or extending the rule to every town, needs far more evidence. inductive-reasoning-s07-q03 Samples justify comparing observed rates, nothing stronger. They cannot certify a zero-fault machine or predict any single bolt with certainty. inductive-reasoning-s07-q04 A consistent difference in one trial supports a local association. Universal or causal claims need repeated trials under varied, controlled conditions. inductive-reasoning-s07-q05 A short consistent run raises the probability that the pattern repeats, but induction never turns 'has happened five times' into a guarantee or an exact figure. inductive-reasoning-s07-q06 An inductive generalisation is only as good as its sample. Times of day that were never sampled may behave differently, so the conclusion should stay limited to weekday mornings. inductive-reasoning-s07-q07 Personal records support a personal association. They cannot establish a universal law about all students, nor promise any particular future result. inductive-reasoning-s07-q08 Near-equal frequencies in a large sample point to roughly equal proportions: an estimate, not an exact count. Expecting the next draw to 'balance things out' is the gambler's fallacy. inductive-reasoning-s07-q09 600 metres is four steps of 150, so about four degrees of cooling. The word 'roughly' matters, because an induced rate supports an estimate rather than a promise. inductive-reasoning-s07-q10 When one category dominates the data, its dominance alone can explain its lead in any subcategory. Comparing rates (late returns per borrowing) rather than raw counts is the fix. inductive-reasoning-s08-q01 The cells count upwards by one, left to right and row by row, so the final cell is 9. inductive-reasoning-s08-q02 In every row the third number is the sum of the first two (2+5=7, 3+6=9), so 4 + 7 = 11. inductive-reasoning-s08-q03 Every number doubles as you move down its column (2→4→8, 3→6→12), so the last column runs 5 → 10 → 20. inductive-reasoning-s08-q04 Each row's third number is the product of the first two (2×3=6, 4×2=8), so 3 × 5 = 15. Test sum, difference, and product rules against every complete row before answering. inductive-reasoning-s08-q05 Every row and every column uses each shade exactly once, a Latin-square rule, and black is the only shade missing from both the third row and the middle column. inductive-reasoning-s08-q06 Each complete row sums to 15 (4+9+2 and 3+5+7), so the last row needs 15 − 8 − 1 = 6. inductive-reasoning-s08-q07 Away from the edges, each cell equals the cell above it plus the cell to its left (4 = 2 + 2, 7 = 3 + 4, 7 = 4 + 3), so the corner is 7 + 7 = 14. inductive-reasoning-s08-q08 The columns list the alphabet in order (A-B-C, D-E-F, G-H-...), so the final column ends with I. inductive-reasoning-s08-q09 In each row the right-hand number is half the left-hand one: 10 ÷ 2 = 5. inductive-reasoning-s08-q10 Each row's third number is the first minus the second (9−4=5, 12−5=7), giving 15 − 6 = 9, and the final column's own climb (5, 7, 9) confirms it. Converging rules are strong evidence you have the right answer. inductive-reasoning-s09-q01 Each output is double the input plus one (3→7, 5→11, 8→17), so 10 × 2 + 1 = 21. Always confirm a candidate rule against every example pair, not just the first. inductive-reasoning-s09-q02 Every output is half its input, so 26 ÷ 2 = 13. inductive-reasoning-s09-q03 Each letter shifts one place forward (L→M, A→B, M→N, P→Q), so GATE becomes HBUF. inductive-reasoning-s09-q04 Each output is double the input minus one, a rule all four examples satisfy, so 9 × 2 − 1 = 17. inductive-reasoning-s09-q05 Each number maps to the letter at that position of the alphabet, and the 11th letter is K. inductive-reasoning-s09-q06 Every output is six times its input, so 11 × 6 = 66. inductive-reasoning-s09-q07 The code reverses the word's letters, so BUS becomes SUB. inductive-reasoning-s09-q08 Each output is the input cubed (2³=8, 3³=27, 4³=64), so 5³ = 125. inductive-reasoning-s09-q09 Each output is triple the input plus one (3→10, 6→19, 10→31), so 12 × 3 + 1 = 37. inductive-reasoning-s09-q10 Each output is the sum of the input's digits (2+3=5, 4+7=11, 6+5=11, 8+1=9), so 7 + 6 = 13. When arithmetic on the whole number fails, try operating on its digits. inductive-reasoning-s10-q01 The gaps double each time (2, 4, 8, 16), so the next gap is 32: 34 + 32 = 66. inductive-reasoning-s10-q02 The gaps rise by two each step (4, 6, 8, 10), so the next gap is 12: 30 + 12 = 42. Equivalently, the nth term is n × (n + 1). inductive-reasoning-s10-q03 Inductive strength grows with sample size, random selection, and a conclusion that stays close to the evidence. Tiny samples, single snapshots, and interested sources all weaken an inference. inductive-reasoning-s10-q04 Short runs fit many possible rules, and real processes meet limits that flatten early trends. Extending a three-point pattern five more steps is the classic extrapolation trap. inductive-reasoning-s10-q05 In every pair the second number is the square of the first, and 36 is 6 squared. Note the pattern skips a value. The rule linking the pair matters, not the row count. inductive-reasoning-s10-q06 Each term is one more than a prime number (2, 3, 5, 7, 11, 13, 17, 19), so the next is 23 + 1 = 24. Mapping an odd-looking sequence onto a familiar number family is a powerful inductive move. inductive-reasoning-s10-q07 Induction strengthens most when new evidence comes from varied, previously unsampled parts of the population, rechecking the same cases adds almost nothing. inductive-reasoning-s10-q08 Two rules run in parallel: the letter steps back two places (Z, X, V, T, R) while the number doubles (1, 2, 4, 8, 16). inductive-reasoning-s10-q09 The multiplier grows by one at each step (×2, ×3, ×4, ×5), so the next step is ×6: 120 × 6 = 720. inductive-reasoning-s10-q10 Testing candidates against all the data is the heart of induction: doubling fits only the first three terms, but the growing-gap rule (+2, +4, +6, +8) survives every step. Source: https://learn.novusstreamsolutions.com/cognitive-skills/inductive-reasoning