Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 7

Question 1

A square piece of paper is folded in half (bringing the top edge to the bottom edge), then in half again (left edge to right edge).
A small triangle is cut from the single closed corner (all folds meet here).
When unfolded, the cutout forms a:

Accepted Answer

Diamond (rhombus) shape at the center

Answer

Triangle at one corner

Answer

Four small triangles at the four corners

Answer

Square in the center

Question 2

A 3×3×3 cube painted on all outer faces is cut into 27 unit cubes. How many unit cubes have exactly 0 painted faces?

Accepted Answer

1

Answer

0

Answer

6

Answer

8

Question 3

On a standard die, if 2 is on top and 3 faces you (toward the south), which number faces east (to your right)?

Accepted Answer

6

Answer

4

Answer

1

Answer

5

Question 4

A rectangular paper is folded so that the shorter edges meet. Then it is folded again the same way. Three holes are punched through all layers in a row. When fully unfolded, how many holes are there?

Accepted Answer

12

Answer

6

Answer

8

Answer

3

Question 5

A cube is viewed from the top-right-front corner, revealing 3 faces. The top face shows a circle, the front face shows a triangle, the right face shows a square. When the cube is flipped upside down (rotated 180° around the front-back axis), what shape appears on the new top face?

Accepted Answer

The symbol on the original bottom face (opposite circle)

Answer

Circle

Answer

Triangle

Answer

Square

Question 6

A 5×5×5 cube is painted on all outer faces, then cut into 125 unit cubes. How many unit cubes have no painted faces?

Accepted Answer

27

Answer

8

Answer

1

Answer

64

Question 7

A die with 1 on top and 2 facing east is tipped north (away from you) twice in a row (two 90° tilts northward). What number is now on top?

Accepted Answer

6

Answer

5

Answer

2

Answer

1