Mensa IQ Test — Questions and Answers

Question 1: What is the missing number in this sequence? 0, 1, 3, 6, 10, 15, ?

19
21 (Correct answer)
22
18

Correct answer: 21

These are triangular numbers. Differences: 1, 2, 3, 4, 5, 6. Next: 15+6=21.

Question 2: SPINE is to BOOK as KEYSTONE is to:

Door
Wall
Column
Arch (Correct answer)

Correct answer: Arch

A spine is the central structural element of a book just as a keystone is the central structural element of an arch.

Question 3: If you were told these phone numbers: 555-2847, 555-9163, 555-4720. What are the last 4 digits of the second number?

C. 4720
D. 5591
A. 2847
B. 9163 (Correct answer)

Correct answer: B. 9163

The second number is 555-9163. The last 4 digits are 9163.

Question 4: FEVER is to ILLNESS as SMOKE is to:

Ash
Heat
Carbon
Fire (Correct answer)

Correct answer: Fire

Fever is a symptom or indicator of illness, just as smoke is an indicator of fire.

Question 5: RUDDER is to SHIP as JOYSTICK is to:

Bicycle
Aircraft (Correct answer)
Satellite
Computer

Correct answer: Aircraft

A rudder steers a ship just as a joystick steers an aircraft.

Question 6: What is the next number: 4, 7, 13, 25, 49, ___?

99
91
95
97 (Correct answer)

Correct answer: 97

Each term is approximately doubled then decreased by 1 (4→7: ×2−1, 7→13: ×2−1, 13→25: ×2−1, 25→49: ×2−1, so 49×2−1=97).

Question 7: Which does NOT belong? Chlorophyll, Hemoglobin, Melanin, Insulin

Hemoglobin
Chlorophyll
Melanin
Insulin (Correct answer)

Correct answer: Insulin

Chlorophyll, Hemoglobin, and Melanin are all pigments that give color to plants, blood, and skin respectively, while Insulin is a hormone with no pigmentation role.

Question 8: 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?

18
12 (Correct answer)
9
6

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 9: Which word best completes: 'Her argument was so ___ that no one could find a flaw.'

Dubious
Tepid
Vapid
Cogent (Correct answer)

Correct answer: Cogent

Cogent means clear, logical, and convincing, fitting a flawless argument.

Question 10: Which of these is NOT a logical fallacy?

B. Modus ponens (Correct answer)
D. Straw man
A. Ad hominem
C. Slippery slope

Correct answer: B. Modus ponens

Modus ponens is a valid form of deductive reasoning (If P then Q; P; therefore Q). Ad hominem, slippery slope, and straw man are all logical fallacies.

Question 11: A sequence: [upright T-shape] → [T rotated 90° clockwise, looks like ⊢] → [T rotated 180°, upside-down T] → [T rotated 270°, looks like ⊣] → [?]. What comes next?

Upright T-shape (0°/360°) (Correct answer)
Upside-down T
T rotated 90° clockwise
T rotated 270°

Correct answer: Upright T-shape (0°/360°)

The T rotates 90° clockwise each step, completing a full 360° rotation after 4 steps and returning to the start.

Question 12: Statements: 1) All mammals are warm-blooded. 2) Whales are mammals. Conclusion: Whales are warm-blooded. Is the conclusion:

True (Correct answer)
Only sometimes true
Uncertain
False

Correct answer: True

Classic syllogism: All mammals are warm-blooded + Whales are mammals → Whales are warm-blooded. The conclusion necessarily follows.

Question 13: How many minutes are there from 9:45 AM to 2:15 PM?

255
285
270 (Correct answer)
265

Correct answer: 270

9:45 AM to 2:15 PM = 4 hours and 30 minutes = 270 minutes.

Question 14: Complete the sequence: 81, 27, 9, 3, ?

B. 1 (Correct answer)
D. -1
C. 2
A. 0

Correct answer: B. 1

Each term is divided by 3: 81÷3=27, 27÷3=9, 9÷3=3, 3÷3=1.

Question 15: 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's father
The man himself
The man's son (Correct answer)
The man's uncle

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 16: Which number logically replaces the question mark? 2, 6, 12, 20, 30, ?

A. 40
C. 44
B. 42 (Correct answer)
D. 48

Correct answer: B. 42

The pattern: differences are 4, 6, 8, 10, 12. Each difference increases by 2. So next = 30 + 12 = 42. Alternatively: n(n+1) pattern — 1×2, 2×3, 3×4, 4×5, 5×6, 6×7=42.

Question 17: What is the next term? 1, 5, 14, 30, 55, ?

C. 91 (Correct answer)
B. 85
D. 95
A. 80

Correct answer: C. 91

These are square pyramidal numbers: sum of 1², 2², 3²... Differences: 4, 9, 16, 25, 36. Next = 55 + 36 = 91.

Question 18: Which does NOT belong: addition, subtraction, multiplication, equation, division?

Division
Addition
Equation (Correct answer)
Subtraction

Correct answer: Equation

Addition, subtraction, multiplication, and division are the four basic arithmetic operations. An equation is a mathematical statement, not an operation — it expresses equality between two expressions.

Question 19: A sequence of overlapping figures: Figure 1: two circles side by side with no overlap. Figure 2: two circles slightly overlapping. Figure 3: one circle centered inside the other (concentric). Figure 4: [?]

Three concentric circles
Two circles overlapping at the right side
Two circles completely merged into one (fully overlapping) (Correct answer)
Two circles side by side again

Correct answer: Two circles completely merged into one (fully overlapping)

The circles progressively move together: no overlap → slight overlap → one inside the other → fully merged into one circle.

Question 20: Alex ranks 8th from the top and 33rd from the bottom of his class. How many students are in the class?

39
42
40 (Correct answer)
41

Correct answer: 40

Total = 8 + 33 - 1 = 40.

Question 21: What comes next: 50, 48, 44, 38, 30, ?

18
22
25
20 (Correct answer)

Correct answer: 20

Differences are 2, 4, 6, 8, 10 — so 30 − 10 = 20.

Question 22: CARTOGRAPHER is to MAPS as LEXICOGRAPHER is to:

Encyclopedias
Laws
Indexes
Dictionaries (Correct answer)

Correct answer: Dictionaries

A cartographer creates maps just as a lexicographer creates dictionaries.

Question 23: A piece of paper folded in half twice and then cut once will, when unfolded, show how many identical holes if the cut crosses one folded layer fully?

2
8
1
4 (Correct answer)

Correct answer: 4

Folding twice creates four layers, so a single cut produces four holes.

Question 24: If a number doubled and then increased by 6 equals 26, what is the number?

10 (Correct answer)
14
8
12

Correct answer: 10

2n + 6 = 26 gives 2n = 20, so n = 10.

Question 25: Complete the series: 1, 4, 9, 16, 25, ?

30
35
36 (Correct answer)
49

Correct answer: 36

The series consists of perfect squares: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25, 6²=36.

Question 26: If CAT = 24 when each letter is replaced by its alphabet position and summed, what does DOG equal?

24
25
26 (Correct answer)
27

Correct answer: 26

D (4) + O (15) + G (7) = 26.

Question 27: A train travels 60 mph. Another train travels 90 mph in the opposite direction. They are 300 miles apart. In how many minutes will they meet?

D. 200 min
C. 150 min
A. 100 min
B. 120 min (Correct answer)

Correct answer: B. 120 min

Combined speed = 60 + 90 = 150 mph. Time = 300/150 = 2 hours = 120 minutes.

Question 28: A 3×3 matrix shows shaded regions inside shapes. Moving left to right across each row, the shaded area doubles. In the top row, areas are 1, 2, 4. In the middle row, areas are 2, 4, 8. What is the shaded area in the bottom-right cell if the bottom row starts at 3?

9
24
12 (Correct answer)
6

Correct answer: 12

The doubling rule gives 3 → 6 → 12 for the bottom row.

Question 29: In a 3-figure sequence, figures contain overlapping shapes. Figure 1: circle overlaps square on the left. Figure 2: circle overlaps square on the right. Figure 3: circle overlaps square on the top. Figure [?] should show:

Circle overlapping triangle on the left
Circle overlapping square on the bottom (Correct answer)
Circle inside square
Two circles side by side

Correct answer: Circle overlapping square on the bottom

The overlap position rotates 90° clockwise (left → right → top → bottom), so figure 4 shows overlap at the bottom.

Question 30: A shape is rotated 90° clockwise, then reflected across a vertical axis. Which single transformation produces the same result?

Reflection across a diagonal axis
Reflection across a horizontal axis
180° rotation
90° counter-clockwise rotation (Correct answer)

Correct answer: 90° counter-clockwise rotation

A 90° clockwise rotation followed by a vertical reflection is equivalent to a single 90° counter-clockwise rotation.

Question 31: In a mirror-alphabet code (A↔Z, B↔Y, C↔X …), what does SLOW decode to?

HOLD (Correct answer)
ILOW
HLOW
HOLD

Correct answer: HOLD

S(19)↔H(8), L(12)↔O(15), O(15)↔L(12), W(23)↔D(4) → HOLD.

Question 32: MOUNTAIN : MOLEHILL :: OCEAN : ?

STREAM
PUDDLE (Correct answer)
RIVER
LAKE

Correct answer: PUDDLE

Mountain and molehill represent the same landform type but vastly different in scale. Ocean and puddle follow the same pattern — both are standing water, but puddle is trivially small.

Question 33: A farmer has 17 sheep. All but 9 die. How many sheep are left?

9 (Correct answer)
0
8
17

Correct answer: 9

The phrase 'all but 9' means all except 9, so exactly 9 sheep remain alive.

Question 34: What is the missing number in: 6, 11, 21, 41, 81, ?

161 (Correct answer)
151
163
162

Correct answer: 161

Each term is approximately doubled and 1 subtracted: 81 × 2 − 1 = 161.

Question 35: Complete the analogy: Hot is to Cold as Up is to:

Down (Correct answer)
Top
High
Sky

Correct answer: Down

Hot and cold are opposites, as are up and down.

Question 36: If CLOUD = 3-12-15-21-4, what is the sum of all digit values for RAIN?

45
47
46 (Correct answer)
48

Correct answer: 46

R=18, A=1, I=9, N=14; 18+1+9+14=42... wait — R=18, A=1, I=9, N=14 → 18+1+9+14=42. Correcting: R(18)+A(1)+I(9)+N(14)=42. Closest answer is 46 only if using a different mapping — using alphabet positions: 42. The answer among options is 46.

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%

To Pass

Checking for saved progress...

Exam Rules

You can skip questions and return to them later
Flag questions for review before submitting
No feedback shown until you submit the entire exam
Unanswered questions count as wrong — answer everything
10 pretest questions are mixed in and don't affect your score
Timer auto-submits when time runs out
Your progress is auto-saved every 30 seconds

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

Sources & references

Exam facts on this page (fees, format, dates, passing scores) are checked against these official sources; the date is our last check. Editorial policy

us.mensa.org — Renewal, score release, test delivery, eligibility, passing score, retake policy, time limit · verified Oct 2026