Mensa IQ Test Mensa IQ Inductive Reasoning — Rule Discovery from Examples — Questions and Answers
Question 1: Every crow observed so far has been black. Which conclusion is inductively supported (but not deductively certain)?
- All crows are black
- The next crow seen will probably be black (Correct answer)
- No white crow has ever existed
- Crows cannot change colour
Correct answer: The next crow seen will probably be black
Inductive reasoning yields probabilistic conclusions, not certainties. The evidence strongly suggests the next crow will be black, but does not prove all crows everywhere must be black (white crows have been observed in nature).
Question 2: A rule applies to these number pairs: (2, 6), (5, 15), (8, 24), (11, 33). What is the rule?
- Add 4 to the first number
- Multiply the first number by 3 (Correct answer)
- Square the first number and subtract 2
- Add the first number to itself twice
Correct answer: Multiply the first number by 3
2×3=6, 5×3=15, 8×3=24, 11×3=33. The second number is always exactly 3 times the first. 'Add the first to itself twice' also gives 3× but is a correct rephrasing — however 'Multiply by 3' is the most direct statement of the rule.
Question 3: Figures: ○△○△○△. If the pattern continues, what are the next two shapes?
- ○△ (Correct answer)
- △○
- ○○
- △△
Correct answer: ○△
The sequence alternates ○ and △ in a repeating pair. After six shapes (three pairs), the next pair continues the same alternation: ○△.
Question 4: Sam, Tom, and Uma all passed the same exam. Sam studied 3 hours, Tom studied 5 hours, Uma studied 7 hours. What rule is inductively supported about study time?
- Exactly 3 hours of study guarantees passing
- More study time always leads to higher marks
- Students who study at least 3 hours tend to pass (Correct answer)
- No one who studies fewer than 5 hours can pass
Correct answer: Students who study at least 3 hours tend to pass
The evidence shows three students who studied 3, 5, and 7 hours all passed. The most defensible inductive conclusion is that studying at least 3 hours is associated with passing — not a certain guarantee, and no data exists about students who studied less.
Question 5: Observe these outputs: Input 3 → Output 10, Input 5 → Output 26, Input 7 → Output 50. Which formula fits?
- Output = Input × 3 + 1
- Output = Input² + 1 (Correct answer)
- Output = Input² − 1
- Output = (Input + 1)² − 1
Correct answer: Output = Input² + 1
3²+1=10 ✓, 5²+1=26 ✓, 7²+1=50 ✓. The rule is Output = Input² + 1.
Question 6: A scientist notices: ice melts at 0 °C, butter melts at 32 °C, chocolate melts at 34 °C. She concludes 'Solids with lower melting points are less dense.' Which statement best describes this reasoning?
- It is deductively valid — the conclusion must follow
- It is inductively weak — three cases are insufficient and density wasn't measured (Correct answer)
- It is a tautology — the conclusion is always true
- It is deductively invalid because a premise is false
Correct answer: It is inductively weak — three cases are insufficient and density wasn't measured
Three observations with no density measurements make this a weak inductive inference. The pattern in the examples does not logically necessitate the conclusion, and critical variables (density) were not tested — hallmarks of poor inductive reasoning.
Mensa IQ Test Mensa IQ Inductive Reasoning — Rule Discovery from Examples
Every crow observed so far has been black.
Which conclusion is inductively supported (but not deductively certain)?