GCAT Spatial Visualization Tasks 4

Question 1

A square piece of cardboard is cut diagonally in half to make two triangles. The two triangles are rearranged to form a rectangle (not a square). What are the proportions of the rectangle?

Accepted Answer

1:2

Answer

Two right isosceles triangles from a square reassemble into a rectangle with length twice the width (ratio 2:1), or equivalently 1:2.

Question 2

Looking at a transparent box from above, you see a 4×3 rectangle. Looking from the front, you see a 4×2 rectangle. What are the dimensions of the box?

Accepted Answer

4×3×2

Answer

Top view (4×3) gives length and width; front view (4×2) gives length and height, so the box is 4 long, 3 wide, and 2 tall.

Question 3

A sphere is cut by a single flat plane. What shape is the cross-section always?

Accepted Answer

A circle

Answer

Any flat plane cutting through a sphere always produces a circular cross-section, regardless of angle.

Question 4

You travel 3 miles north, then 4 miles east. How far are you in a straight line from your starting point?

Accepted Answer

5 miles

Answer

Using the Pythagorean theorem: √(3² + 4²) = √(9 + 16) = √25 = 5 miles.

Question 5

A square is rotated 45° and placed inside a larger square so that its corners touch the midpoints of the larger square's sides. What fraction of the larger square does the rotated square cover?

Accepted Answer

1/2

Answer

A square rotated 45° with corners at the midpoints of a larger square covers exactly half the larger square's area.

GCAT - General Cognitive Ability Test Practice Test

GCAT - General Cognitive Ability Test Practice Test

GCAT Spatial Visualization Tasks 4