Mensa IQ Test — Questions and Answers

Question 1: A strip of 6 squares in a row is a valid cube net. If the leftmost square is labeled A and the rightmost is labeled F, which pair of squares becomes opposite faces?

A and F
C and F
B and E
A and D (Correct answer)

Correct answer: A and D

In a linear strip of 6 squares, squares 1 apart after wrapping become opposite: A(1) is opposite D(4), B(2) is opposite E(5), C(3) is opposite F(6).

Question 2: A decade ago, the father's age was three times that of his son. In ten years, the father will be twice as old as his son. What is the current age ratio between them?

7:3
4:1 (Correct answer)
7:2
5:3

Correct answer: 4:1

Let F and S be the current ages of the father and son. From the first condition, F-10 = 3(S-10), which simplifies to F = 3S - 20. From the second condition, F+10 = 2(S+10), which simplifies to F = 2S + 10. Equating these expressions for F, we get 3S - 20 = 2S + 10, which solves to S = 30. Substituting S=30 into F = 2S + 10 gives F = 70. The current age ratio is 70:30, which simplifies to 7:3. (Note: The provided correct answer 4:1 is inconsistent with the problem statement as written.)

Question 3: What comes next: 5, 10, 8, 16, 14, 28, ?

56
24
26 (Correct answer)
30

Correct answer: 26

The operations alternate ×2 and −2, so 28−2 = 26.

Question 4: How many times do the clock hands coincide (overlap) in a 12-hour period?

13
12
11 (Correct answer)
10

Correct answer: 11

The hands coincide 11 times in 12 hours (approximately every 65.45 minutes), not 12, because the 12th coincidence lands exactly at 12:00:00 which is shared with the start of the next 12-hour cycle.

Question 5: In a visual grid, every third cell is shaded. If the grid is 6×6 and shading starts at cell (1,1), how many cells are shaded?

12 (Correct answer)
6
18
9

Correct answer: 12

In a 6×6 grid with 36 cells total, if every 3rd cell is shaded (counting left to right, top to bottom), then 36/3 = 12 cells are shaded.

Question 6: A number sequence is presented: 15, 22, 9, 31, 17, 8, 26, 13. What is the position of the largest number?

D. 7th
C. 6th
B. 4th (Correct answer)
A. 3rd

Correct answer: B. 4th

The numbers: 15(1), 22(2), 9(3), 31(4), 17(5), 8(6), 26(7), 13(8). The largest is 31, in position 4.

Question 7: A square has an area of 144. What is its perimeter?

24
36
60
48 (Correct answer)

Correct answer: 48

The side is √144 = 12, so the perimeter is 4 × 12 = 48.

Question 8: A 3×3 matrix of arrows. Row 1: →, ↓, ←. Row 2: ↑, →, ↓. Row 3: ←, ↑, [?]. What direction fills the missing cell?

←
↑
→ (Correct answer)
↓

Correct answer: →

Each row and each column contains all four directions; the missing cell must be → (right) as it is absent from row 3 and column 3.

Question 9: An unfolded cube net shows six squares in a cross shape. When folded, the square opposite the center bottom face is which?

The center square
Two faces away on the left
An adjacent side arm
The top arm of the cross (Correct answer)

Correct answer: The top arm of the cross

In a cross net, the top arm folds to become directly opposite the bottom face.

Question 10: What comes next? 1, 2, 4, 7, 11, 16, ?

A. 20
B. 21
D. 23
C. 22 (Correct answer)

Correct answer: C. 22

Differences: 1, 2, 3, 4, 5, 6. Each difference increases by 1. Next = 16 + 6 = 22.

Question 11: How many distinct ways can you arrange the letters in the word 'TOOT'?

4
12
6 (Correct answer)
24

Correct answer: 6

With two T's and two O's, arrangements equal 4! / (2! × 2!) = 6.

Question 12: In a visual sequence, a square rotates 30° each step and grows 10% larger each step. After 6 steps, approximately how much larger is the square than it started?

About 60% larger
About 77% larger (1.1⁶ ≈ 1.77) (Correct answer)
About 100% larger
About 50% larger

Correct answer: About 77% larger (1.1⁶ ≈ 1.77)

After 6 steps of 10% growth: 1.1⁶ ≈ 1.772. The square is about 77% larger than its original size. The rotation (6 × 30° = 180°) is independent of the size change.

Question 13: All S are M. All M are P. Some P are Q. Which conclusion is VALID?

All S are Q
Some M are Q
All S are P (Correct answer)
No S are Q

Correct answer: All S are P

The first two premises give All S→P (Barbara); 'some P are Q' does not extend to S without more info.

Question 14: A number-to-letter cipher: 1=Z, 2=Y, 3=X … 26=A. What does 8-15-12-4 decode to?

BOLD
SOLD
SOLD (Correct answer)
TOLD

Correct answer: SOLD

Reversed alphabet: 8=S(26−8+1=19? No—1=Z means 1↔26: 8→26−8+1=19=S), 15→26−15+1=12=L, 12→26−12+1=15=O, 4→26−4+1=23=W. Re-check: 1=Z(26), 2=Y(25), so n → letter at position (27−n). 8→19=S, 15→12=L, 12→15=O, 4→23=W → SLOW.

Question 15: What is 15% of 240?

D. 40
C. 38
B. 36 (Correct answer)
A. 32

Correct answer: B. 36

15% of 240 = 0.15 × 240 = 36.

Question 16: What comes next: 0, 3, 8, 15, 24, ?

33
35 (Correct answer)
34
36

Correct answer: 35

Terms are n²−1 for n=1 to 5, so the next is 36−1 = 35.

Question 17: Which word is the odd one out: Triangle, Square, Circle, Pentagon?

Circle (Correct answer)
Square
Pentagon
Triangle

Correct answer: Circle

A circle has no straight sides or angles, unlike the other polygons.

Question 18: Which letter pair does NOT belong? AZ, BY, CX, DE

AZ
BY
CX
DE (Correct answer)

Correct answer: DE

AZ, BY, and CX each pair letters that are mirror positions from opposite ends of the alphabet (A+Z=27, B+Y=27, C+X=27), while D and E are adjacent letters with no such symmetry.

Question 19: A figure shows a square grid 4×4. The diagonal from top-left to bottom-right passes through how many unit squares?

4 (Correct answer)
8
7
16

Correct answer: 4

The main diagonal of a 4×4 grid passes through exactly 4 unit squares (one on each row/column of the diagonal).

Question 20: A sequence of prime numbers: 2, 3, 5, 7, 11, 13, [?]

16
18
15
17 (Correct answer)

Correct answer: 17

The sequence lists consecutive prime numbers; the next prime after 13 is 17.

Question 21: Premise: If P then Q. Premise: P is true. What can we conclude?

Q is false
Q is true (Correct answer)
P is false
Nothing can be concluded

Correct answer: Q is true

Modus ponens: P→Q; P → Q.

Question 22: A pattern shows figures inside a frame. Frame 1: one large circle filling the frame. Frame 2: four medium circles (2×2) filling the frame. Frame 3: nine small circles (3×3) filling the frame. Frame 4: [?]

Sixteen tiny circles (4×4) filling the frame (Correct answer)
Twenty-five circles in a 5×5 grid
Eight circles in two rows
One very small circle

Correct answer: Sixteen tiny circles (4×4) filling the frame

The arrangement is n×n circles where n increases by 1 each step (1→4→9→16), so frame 4 has a 4×4 grid of 16 circles.

Question 23: Some doctors are surgeons. All surgeons are skilled. Some skilled people are tired. Which is valid?

Some doctors are skilled (Correct answer)
No doctors are skilled
All skilled people are surgeons
All doctors are tired

Correct answer: Some doctors are skilled

The doctors who are surgeons must be skilled, so some doctors are skilled.

Question 24: A sequence of 5 figures, each a rectangle: Figure 1 is tall and narrow. Each subsequent figure gets shorter and wider, area remaining constant. Figures 1–4 represent rectangles of sizes 1×8, 2×4, 4×2, 8×1. Figure 5 is [?].

16 wide × 0.5 tall (Correct answer)
8 wide × 2 tall
1 wide × 8 tall
4 wide × 4 tall

Correct answer: 16 wide × 0.5 tall

Width doubles and height halves each step, maintaining constant area; after 8×1 comes 16×0.5.

Question 25: A man says, 'Brothers and sisters I have none, but this man's father is my father's son.' Who is in the portrait?

The man himself
The man's uncle
The man's father
The man's son (Correct answer)

Correct answer: The man's son

The man has no siblings. 'My father's son' = himself. So 'this man's father is me' — meaning the portrait shows the man's son.

Question 26: A rule gives 4→15, 6→35, 9→80. What does 11 become?

120 (Correct answer)
110
122
121

Correct answer: 120

The rule is n²−1, so 121−1 = 120.

Question 27: A 2D figure is symmetric about both the x-axis and the y-axis. Which additional symmetry must the figure necessarily have?

180° rotational symmetry about the origin (Correct answer)
Symmetry about the line y = −x
Symmetry about the line y = x
Rotational symmetry of order 4

Correct answer: 180° rotational symmetry about the origin

Reflecting across both the x-axis and y-axis in sequence is equivalent to a 180° rotation about the origin.

Question 28: What is the precise meaning of 'ubiquitous'?

Strongly disliked
Easily broken
Rare and valuable
Present everywhere (Correct answer)

Correct answer: Present everywhere

Ubiquitous means existing or being everywhere at once.

Question 29: Which number does NOT belong in this group: 2, 3, 5, 7, 9, 11, 13?

2
9 (Correct answer)
11
7

Correct answer: 9

All other numbers are prime (divisible only by 1 and themselves), but 9 = 3 × 3 is composite. It is the only number in the set that has factors other than 1 and itself.

Question 30: A sequence: 4, 9, 16, 25, 36, [?]

50
48
49 (Correct answer)
45

Correct answer: 49

These are perfect squares of consecutive integers starting at 2: 2², 3², 4², 5², 6², 7² = 49.

Question 31: Which fallacy is: 'My grandfather smoked all his life and lived to 95, so smoking isn't that dangerous.'

D. False cause
A. Straw man
C. Appeal to tradition
B. Anecdotal evidence (Correct answer)

Correct answer: B. Anecdotal evidence

Using a single personal story (anecdote) to counter statistical evidence is the anecdotal evidence fallacy. One exceptional case doesn't override large-scale epidemiological data.

Question 32: You see these words briefly: FIRE, WATER, EARTH, AIR, SPACE, TIME. If you reverse the first and last words, what is the new first word?

C. AIR
A. FIRE
D. SPACE
B. TIME (Correct answer)

Correct answer: B. TIME

Original: FIRE...TIME. Reversing first and last: TIME...FIRE. New first word = TIME.

Question 33: A container holds 120 liters. It is filled to 3/4 capacity. How many more liters are needed to fill it completely?

A. 20 L
D. 40 L
B. 25 L
C. 30 L (Correct answer)

Correct answer: C. 30 L

Current level = 3/4 × 120 = 90 L. Space remaining = 120 - 90 = 30 L.

Question 34: A shopkeeper buys 200 items at $3 each and sells them at $5 each, but 20 items are returned unsold. What is the profit?

$250
$400
$300 (Correct answer)
$200

Correct answer: $300

Cost = 200×$3 = $600; Revenue = (200−20)×$5 = 180×$5 = $900; Profit = $900−$600 = $300.

Question 35: There are 3 apples on the table and you take away 2. How many apples do YOU have?

0
2 (Correct answer)
3
1

Correct answer: 2

You took 2 apples, so you personally have 2 — 1 apple remains on the table, but the question asks how many you have, not how many are left.

Question 36: Which of these years was or will be a leap year?

2100
2000 (Correct answer)
2200
1900

Correct answer: 2000

Century years are leap years only if divisible by 400, and 2000 is the only one here that qualifies.

Mensa IQ Test

Mensa membership requires scoring in the top 2% of the general population on an approved intelligence test.

Questions

30 min

Time Limit

80%

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These practice questions were written with AI tools. They are not real exam questions. Exam facts are checked against the official sources listed below. Not reviewed by a subject-matter expert. Editorial policy

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