Mensa Mensa IQ Spatial and Abstract Reasoning Questions and Answers 3 — Questions and Answers
Question 1: A cube is painted red on all faces, then cut into 27 equal smaller cubes. How many small cubes have exactly 2 red faces?
- 8
- 12 (Correct answer)
- 6
- 4
Correct answer: 12
Edge cubes (not corner) have exactly 2 painted faces; a 3×3×3 cube has 12 such edges.
Question 2: Which number replaces the question mark? 2, 6, 18, 54, ?
- 108
- 162 (Correct answer)
- 72
- 216
Correct answer: 162
Each term is multiplied by 3: 54 × 3 = 162.
Question 3: A square sheet of paper is folded in half diagonally, then folded in half again. A hole is punched through all layers at the center. How many holes appear when fully unfolded?
- 2
- 4 (Correct answer)
- 1
- 8
Correct answer: 4
Each diagonal fold doubles the hole count, so two folds produce 4 holes.
Question 4: In the sequence: △○□△○□△○?, what shape comes next?
- △
- ○
- □ (Correct answer)
- ◇
Correct answer: □
The repeating pattern is triangle, circle, square, and the next position is the third in that cycle.
Question 5: If a clock shows 3:45, what is the angle between the hour and minute hands?
- 172.5°
- 157.5° (Correct answer)
- 150°
- 165°
Correct answer: 157.5°
Hour hand is at 112.5° and minute hand is at 270°, giving a difference of 157.5°.
Question 6: Which figure is the odd one out? A pentagon with 5 equal sides, a hexagon with 6 equal sides, a square with 4 equal sides, a triangle with 3 equal sides, a circle.
- Pentagon
- Circle (Correct answer)
- Hexagon
- Triangle
Correct answer: Circle
A circle has no straight sides or vertices, making it the only non-polygon in the set.
Question 7: A 3D shape has 6 faces, 12 edges, and 8 vertices. What shape is it?
- Triangular prism
- Cube (Correct answer)
- Octahedron
- Rectangular pyramid
Correct answer: Cube
A cube (and any cuboid) has exactly 6 faces, 12 edges, and 8 vertices per Euler's formula.
Mensa Mensa IQ Spatial and Abstract Reasoning Questions and Answers 3
A cube is painted red on all faces, then cut into 27 equal smaller cubes.
How many small cubes have exactly 2 red faces?