Mensa IQ Test Mensa IQ Inductive Reasoning — Rule Discovery from Examples

Question 1

Every crow observed so far has been black. Which conclusion is inductively supported (but not deductively certain)?

Accepted Answer

The next crow seen will probably be black

Answer

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?

Accepted Answer

Multiply the first number by 3

Answer

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?

Accepted Answer

○△

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?

Accepted Answer

Students who study at least 3 hours tend to pass

Answer

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?

Accepted Answer

Output = Input² + 1

Answer

3²+1=10 ✓, 5²+1=26 ✓, 7²+1=50 ✓. The rule is Output = Input² + 1.

Mensa Practice Test

Mensa Practice Test

Mensa IQ Test Mensa IQ Inductive Reasoning — Rule Discovery from Examples