Mensa Spatial Reasoning 3

Question 1

A cube is painted red on all faces and then cut into 27 equal smaller cubes. How many small cubes have exactly 2 red faces?

Accepted Answer

12

Answer

The 12 edge cubes (not corners) each have exactly 2 painted faces.

Question 2

Which arrangement of 6 squares CANNOT be folded into a cube?

Accepted Answer

A straight 1×6 row

Answer

A straight 1×6 row cannot fold into a cube because opposite faces would overlap.

Question 3

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

Accepted Answer

90° counter-clockwise rotation

Answer

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

Question 4

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?

Accepted Answer

Row 4, Column 2

Answer

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

Question 5

Which 3D shape produces an identical circular cross-section for every cut made parallel to its base?

Accepted Answer

Cylinder

Answer

A cylinder produces a circular cross-section for every cut parallel to its base.

Mensa Practice Test

Mensa Practice Test

Mensa Spatial Reasoning 3