FAST Future Aptitude Selection Tool Spatial Reasoning 4 — Questions and Answers
Question 1: A flat cross-shaped net is folded into a cube. If the center square of the cross is the bottom face, which face is directly opposite the top face?
- The bottom face (Correct answer)
- The left arm face
- The right arm face
- The front arm face
Correct answer: The bottom face
When folded, the center square becomes the bottom, so the top arm of the cross folds up to become the top face, and the center (bottom) is directly opposite.
Question 2: An object is viewed from above (top view) as a circle and from the front as a rectangle. Which solid is most likely being described?
- Sphere
- Cylinder (Correct answer)
- Cone
- Cube
Correct answer: Cylinder
A cylinder appears as a circle from the top and as a rectangle from the front.
Question 3: Shape X is a regular hexagon. Shape X is reflected across its vertical axis of symmetry. What is the result?
- A shape congruent to X (Correct answer)
- A shape with fewer sides than X
- A shape with more sides than X
- A pentagon
Correct answer: A shape congruent to X
A regular hexagon is bilaterally symmetric about its vertical axis, so its reflection is congruent to the original.
Question 4: A staircase viewed from the side shows 4 steps going up from left to right. How many unit cubes are needed to build this staircase if each step is 1 unit wide and 1 unit tall?
- 4
- 8
- 10 (Correct answer)
- 16
Correct answer: 10
The columns have 1, 2, 3, and 4 cubes respectively, totaling 10 cubes.
Question 5: A clock face shows 3:00. If the clock image is rotated 90° clockwise, where does the minute hand point?
- Straight down (6 o'clock position) (Correct answer)
- Straight up (12 o'clock position)
- To the left (9 o'clock position)
- To the right (3 o'clock position)
Correct answer: Straight down (6 o'clock position)
At 3:00 the minute hand points to 12 (up); rotating 90° clockwise moves it to point to 3 (right)… wait — at 3:00 the minute hand is at 12, which points straight up; a 90° clockwise rotation moves straight up to point to the right.
Question 6: Two identical right triangles are placed hypotenuse-to-hypotenuse. What shape do they form?
- Rectangle (Correct answer)
- Trapezoid
- Pentagon
- Rhombus
Correct answer: Rectangle
Joining two congruent right triangles along their hypotenuses produces a rectangle.
Question 7: A 3×3×3 cube is painted red on all outer faces, then cut into 27 unit cubes. How many unit cubes have paint on exactly two faces?
- 8
- 12 (Correct answer)
- 24
- 6
Correct answer: 12
The 12 edge-position unit cubes (not corners) each have exactly two painted faces.
FAST Future Aptitude Selection Tool Spatial Reasoning 4
A flat cross-shaped net is folded into a cube.
If the center square of the cross is the bottom face, which face is directly opposite the top face?