Mensa IQ Test — Questions and Answers

Question 1: If it takes 8 painters 6 days to paint a house, how many days for 12 painters?

9 days
3 days
4 days (Correct answer)
5 days

Correct answer: 4 days

Total work is 48 painter-days, so 48 / 12 = 4 days.

Question 2: A sequence of arrows points: Up, Right, Down, Left, Up, Right, Down, Left, Up, ?

Right (Correct answer)
Up
Down
Left

Correct answer: Right

The cycle (Up, Right, Down, Left) repeats every 4 terms; the 10th term is Right.

Question 3: Next number: 90, 78, 66, 54, ?

44
42 (Correct answer)
40
48

Correct answer: 42

Each term decreases by 12, so 54-12=42.

Question 4: DUSK : DAWN :: EPILOGUE : ?

Appendix
Chapter
Prologue (Correct answer)
Index

Correct answer: Prologue

Dusk is the end of the day and dawn is its beginning; an epilogue is the end of a work and a prologue is its beginning.

Question 5: A grid has rows labeled 1–4 (top to bottom) and columns A–D (left to right). A pattern of shaded cells appears at (1,A), (2,B), (3,C). Which cell logically continues the diagonal?

(4,B)
(4,A)
(4,D) (Correct answer)
(3,D)

Correct answer: (4,D)

The diagonal moves one row down and one column right each step, landing at row 4, column D.

Question 6: A cube net (cross-shaped) has a star on the center square, a circle on the square directly above it, and a triangle on the square directly below it. When folded, what shape is on the face opposite the star?

Triangle
Neither — star has no opposite
Circle (Correct answer)
Square

Correct answer: Circle

In a standard cross-shaped net, the top and bottom extensions fold to become opposite faces, so the circle (above the star) ends up opposite the triangle (below), and the star's opposite is determined by the remaining face — but in this cross layout the square directly above folds to be opposite the square directly below, making the circle opposite the triangle; the star's opposite is the one square to the side not mentioned, but given only these three, circle is on the face opposite triangle, and the face above the center folds to face the center, so the circle faces the star's opposite direction — the circle is opposite the star.

Question 7: Identify the word that means 'to make less severe'.

Amplify
Provoke
Mitigate (Correct answer)
Aggravate

Correct answer: Mitigate

Mitigate means to lessen the seriousness or severity of something.

Question 8: Choose the image that completes the pattern

C
B
D (Correct answer)
A

Correct answer: D

The pattern progresses by increasing the number of sides of the outer polygon by one in each step (triangle, square, pentagon, hexagon). Concurrently, the number of dots inside the polygon also increases by one. Therefore, the next image in the sequence should be a hexagon containing four dots.

Question 9: In a scenario where numbers in a grid relate to each other, find the missing number. Top row: [3, 5, 15]. Middle row: [4, 7, 28]. Bottom row: [6, 2, ?].

10
12 (Correct answer)
14
8

Correct answer: 12

The pattern in each row is that the third number is the product of the first two numbers. In the top row, 3 * 5 = 15. In the middle row, 4 * 7 = 28. Therefore, in the bottom row, the missing number is 6 * 2 = 12.

Question 10: 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?

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

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 11: Complete: 1, 8, 27, 64, ?

144
100
125 (Correct answer)
121

Correct answer: 125

These are cubes (1³,2³,3³,4³,5³), so 5³=125.

Question 12: What reasoning error is: 'We've always done it this way, so we shouldn't change it.'

C. Appeal to authority
B. Appeal to tradition (Correct answer)
D. Bandwagon fallacy
A. Appeal to nature

Correct answer: B. Appeal to tradition

Appeal to tradition argues that something is correct or better simply because it is traditional or has always been done that way. Tradition alone doesn't validate a practice.

Question 13: A clock shows 3:15. What is the angle between the hour and minute hands?

15°
7.5° (Correct answer)
0°
22.5°

Correct answer: 7.5°

At 3:15, the minute hand is at 90° and the hour hand is at 97.5° (3×30 + 15×0.5), giving a difference of 7.5°.

Question 14: Paula finishes before Quinn. Quinn finishes before Rachel. Sam finishes after Rachel. Who finishes third?

Sam
Rachel (Correct answer)
Quinn
Paula

Correct answer: Rachel

The order is Paula, Quinn, Rachel, Sam — Rachel is third.

Question 15: A figure sequence shows a flag on a pole: Step 1: flag on left side of vertical pole. Step 2: flag on right side. Step 3: flag on left side, but larger. Step 4: flag on right side, larger. Step 5: flag on left side, even larger. [?]

Flag on left side, same size
Flag on right side, smaller
Flag on left side, smaller
Flag on right side, even larger (Correct answer)

Correct answer: Flag on right side, even larger

The flag alternates left/right while growing larger every two steps; step 6 continues the right-side position at the larger size.

Question 16: You are in a dark room with one match, a candle, a wood stove, and a gas lamp. Which do you light first?

The candle
The gas lamp
The match (Correct answer)
The wood stove

Correct answer: The match

You must light the match first before you can ignite any other item in the room.

Question 17: Mary is twice as old as Ann was when Mary was as old as Ann is now. Mary is 28. How old is Ann?

D. 18
B. 21 (Correct answer)
C. 24
A. 14

Correct answer: B. 21

Let Ann's current age = A. When Mary was A years old, the age difference (28-A) years ago, Ann was A-(28-A) = 2A-28. Mary is twice that age now: 28 = 2(2A-28) = 4A-56, so 4A = 84, A = 21.

Question 18: In a 3×3 matrix, each row contains shapes of increasing size: small, medium, large. Each column contains a circle, triangle, and square in some order. The bottom-left cell must be which shape if column 1 already has a circle (top) and square (middle)?

Triangle (Correct answer)
Circle
Diamond
Square

Correct answer: Triangle

Each column uses each shape exactly once, so the remaining shape for the bottom of column 1 is a triangle.

Question 19: What comes next: 2, 5, 11, 23, 47, ?

96
94
95 (Correct answer)
93

Correct answer: 95

Each term doubles and adds 1 (×2+1), so 47×2+1=95.

Question 20: Which Roman numeral equals 2,024?

C. MMXXV
B. MMXXIV (Correct answer)
D. MMXXI
A. MMXXIII

Correct answer: B. MMXXIV

MM=2000, XX=20, IV=4. MMXXIV = 2000+20+4 = 2024.

Question 21: If the statement 'All poets are dreamers' is true, which of the following must also be true?

If someone is not a dreamer, they are not a poet (Correct answer)
All dreamers are poets
No poets are dreamers
Some dreamers are not poets

Correct answer: If someone is not a dreamer, they are not a poet

The contrapositive of 'All poets are dreamers' is 'If not a dreamer, then not a poet,' which is logically equivalent.

Question 22: What number follows: 17, 19, 23, 29, 37, ?

43
47 (Correct answer)
45
41

Correct answer: 47

The differences are 2, 4, 6, 8, 10 — even numbers increasing by 2, so 37 + 10 = 47.

Question 23: From the list Dog, 5, Red, Moon, 8, Green — how many COLORS are in the list?

4
3
2 (Correct answer)
1

Correct answer: 2

The list contains two colors: Red and Green.

Question 24: A list of words: CAR, TREE, MOON, FISH, LAMP, BIRD. Which word was in the middle of the list?

A. MOON
B. FISH (Correct answer)
C. LAMP
D. TREE

Correct answer: B. FISH

The list has 6 words. Middle positions are 3rd and 4th: MOON(3rd) and FISH(4th). If one middle word is asked for, FISH is the 4th word — often the second-middle is considered 'the middle'. The answer is FISH.

Question 25: Tom is older than Sam. Sam is older than Kay. Kay is older than Lou. Who is the youngest?

Tom
Kay
Sam
Lou (Correct answer)

Correct answer: Lou

The chain Tom > Sam > Kay > Lou places Lou as the youngest.

Question 26: Notice these numbers: 7, 3, 8, 1, 5, 9, 2, 4, 6. What is the sum of the 2nd and 7th numbers?

D. 12
C. 10
B. 9
A. 5 (Correct answer)

Correct answer: A. 5

2nd number = 3. 7th number = 2. Sum = 3 + 2 = 5.

Question 27: All A are B. All B are C. No C are D. Which conclusion is valid?

Some C are A
All D are A
Some A are D
No A are D (Correct answer)

Correct answer: No A are D

A→B→C and No C→D → No A→D (extended Barbara + Celarent chain).

Question 28: No reptiles are warm-blooded. All snakes are reptiles. Therefore:

Some snakes are warm-blooded
Some reptiles are warm-blooded
All warm-blooded animals are snakes
No snakes are warm-blooded (Correct answer)

Correct answer: No snakes are warm-blooded

EAE-1 (Celarent): No R are W; All S are R → No S are W.

Question 29: Looking at a 4×4 grid from above, a ball starts at the top-left corner (row 1, col 1) and moves 2 squares right, then 3 squares down, then 1 square left. What is the ball's final position?

Row 3, Column 3
Row 4, Column 3
Row 4, Column 2 (Correct answer)
Row 3, Column 2

Correct answer: Row 4, Column 2

Starting at (row 1, col 1): right 2 → col 3; down 3 → row 4; left 1 → col 2, giving row 4, column 2.

Question 30: Which does not belong: Dog, Cat, Lion, Sparrow?

Lion
Cat
Dog
Sparrow (Correct answer)

Correct answer: Sparrow

A sparrow is a bird while the others are mammals.

Question 31: If the statement 'All A are B' is true, which statement must also be true?

Some B are A (Correct answer)
No B are A
All B are A
Some A are not B

Correct answer: Some B are A

If all A are B, then at least some B (namely all the A's) must be A, making 'Some B are A' necessarily true.

Question 32: Each cell in a 3×3 matrix contains a number. Row sums are 6, 12, and 18. Column sums are 9, 9, and 18. What is the value in the bottom-right cell if the bottom row is 3, 6, ?

6
12
18
9 (Correct answer)

Correct answer: 9

The bottom row must sum to 18, and 3+6+x=18 gives x=9.

Question 33: A store offers a 20% discount on an item that originally costs $150. What is the sale price?

B. $120 (Correct answer)
C. $125
D. $130
A. $110

Correct answer: B. $120

Discount = 20% × $150 = $30. Sale price = $150 - $30 = $120.

Question 34: 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?

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

Correct answer: B. TIME

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

Question 35: A 3×3×3 cube is dipped in paint (all outer faces painted), then the top layer of 9 unit cubes is removed. How many of those 9 removed unit cubes have exactly 2 painted faces?

8
0
4 (Correct answer)
1

Correct answer: 4

The top layer has 1 center (1 painted face), 4 edge pieces (2 painted faces each), and 4 corner pieces (3 painted faces each); so 4 unit cubes have exactly 2 painted faces.

Question 36: What is 20% of 20% of 500?

A. 10
D. 25
B. 15
C. 20 (Correct answer)

Correct answer: C. 20

20% of 500 = 100. 20% of 100 = 20.

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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