inductive-reasoning-s01-q01
Each term rises by 2, so the sequence continues 8 + 2 = 10.
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.
Each term rises by 2, so the sequence continues 8 + 2 = 10.
The sequence adds 5 at every step: 20 + 5 = 25.
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.
The sequence falls by 3 each step: 11 − 3 = 8.
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.
Each term adds 3: 11 + 3 = 14.
Each term is half the one before: 8 ÷ 2 = 4.
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.
The amount subtracted shrinks by one each step (−10, −9, −8), so the next step is −7: 63 − 7 = 56.
These are the multiples of 7 in order, so the next is 7 × 5 = 35.
The sequence skips one letter each step (two places forward), so after G comes I.
Each step moves two letters backwards through the alphabet: T back two is R.
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.
The first letter walks forward from A while the second walks backwards from Z, so the pair after DW joins E with V.
The jump grows by one letter each time (+1, +2, +3, +4), so the next jump is five letters: K to P.
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.
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.
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).
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.
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.
The three-shape unit circle–square–triangle repeats, and the second unit still needs its triangle.
The repeating unit is star, star, dot. The seventh symbol starts a new unit, so the second star comes next.
The arrow rotates a quarter turn clockwise each step, so after right it points down.
The dot count climbs through the odd numbers, adding two each time: 7 + 2 = 9.
Size and colour change together in a two-step cycle, so a large white square is always followed by a small black one.
The side count rises by one with each figure, so a seven-sided shape follows the hexagon.
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.
The shading moves one quarter clockwise each step, so after bottom-right it reaches bottom-left.
Two rules run together: the count rises by one each card while the shape alternates between triangle and square, so five triangles come next.
The shared rule is that the dot count equals the number of sides, so a six-sided hexagon should carry six dots, not seven.
8, 64, and 216 are perfect cubes (2³, 4³, 6³); 100 is a square but not a cube.
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.
27, 45, and 63 are all multiples of 9; dividing 35 by 9 leaves a remainder.
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.
Every other pair sums to 10; 5 + 6 makes 11.
Level, civic, and rotor read the same forwards and backwards (palindromes); tiles does not.
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.
In the other triples each number doubles the one before; 8 to 12 adds 4 instead of doubling.
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.
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.
6 is double 3, so apply the same doubling: 7 × 2 = 14.
F sits three letters after C, and three letters after J is M.
The second word spells the first backwards, and flow reversed is wolf. Watch for near-misses that merely rearrange the same letters.
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.
The second number is the square root of the first, and the square root of 64 is 8.
Each letter of the pair moves three places forward: J becomes M and K becomes N.
The second value is the reciprocal of the first, and the reciprocal of 1/8 is 8.
The single number is the sum of the pair: 7 + 6 = 13.
The number counts the shape's sides: a triangle has three and a hexagon has six.
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.
Two strands interleave (1, 2, 3, 4 and 10, 20, 30), and the next position belongs to the tens strand: 40.
Odd positions climb by two (2, 4, 6, 8) while even positions fall by ten; the seventh term continues the climbing strand.
The steps alternate +1, +2, +1, +2; after 12 the next step is +2, giving 14.
Letters skipping one place (A, C, E, G) alternate with even numbers, and the next position is a letter.
One strand falls by five (40, 35, 30, 25) while the other triples (1, 3, 9); the next term triples again: 9 × 3 = 27.
Each term is the sum of the two before it: 5 + 8 = 13. When neither differences nor ratios settle, try combining earlier terms.
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.
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.
Both interleaved strands rise by two (6, 8, 10, 12 and 11, 13, 15); the next term continues the second strand: 17.
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.
Induction supports a probable, local generalisation: many consistent sightings at one lake. Claims about all swans, or about what cannot happen, outrun the evidence.
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.
Samples justify comparing observed rates, nothing stronger. They cannot certify a zero-fault machine or predict any single bolt with certainty.
A consistent difference in one trial supports a local association. Universal or causal claims need repeated trials under varied, controlled conditions.
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.
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.
Personal records support a personal association. They cannot establish a universal law about all students, nor promise any particular future result.
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.
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.
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.
The cells count upwards by one, left to right and row by row, so the final cell is 9.
In every row the third number is the sum of the first two (2+5=7, 3+6=9), so 4 + 7 = 11.
Every number doubles as you move down its column (2→4→8, 3→6→12), so the last column runs 5 → 10 → 20.
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.
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.
Each complete row sums to 15 (4+9+2 and 3+5+7), so the last row needs 15 − 8 − 1 = 6.
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.
The columns list the alphabet in order (A-B-C, D-E-F, G-H-...), so the final column ends with I.
In each row the right-hand number is half the left-hand one: 10 ÷ 2 = 5.
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.
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.
Every output is half its input, so 26 ÷ 2 = 13.
Each letter shifts one place forward (L→M, A→B, M→N, P→Q), so GATE becomes HBUF.
Each output is double the input minus one, a rule all four examples satisfy, so 9 × 2 − 1 = 17.
Each number maps to the letter at that position of the alphabet, and the 11th letter is K.
Every output is six times its input, so 11 × 6 = 66.
The code reverses the word's letters, so BUS becomes SUB.
Each output is the input cubed (2³=8, 3³=27, 4³=64), so 5³ = 125.
Each output is triple the input plus one (3→10, 6→19, 10→31), so 12 × 3 + 1 = 37.
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.
The gaps double each time (2, 4, 8, 16), so the next gap is 32: 34 + 32 = 66.
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 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.
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.
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.
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.
Induction strengthens most when new evidence comes from varied, previously unsampled parts of the population, rechecking the same cases adds almost nothing.
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).
The multiplier grows by one at each step (×2, ×3, ×4, ×5), so the next step is ×6: 120 × 6 = 720.
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.