Basic Ability Test Basic Ability Spatial Reasoning and Visualization 4 — Questions and Answers
Question 1: A figure is rotated 270° clockwise. This is equivalent to a rotation of how many degrees counterclockwise?
- 270°
- 180°
- 90° (Correct answer)
- 45°
Correct answer: 90°
270° clockwise equals 360° − 270° = 90° counterclockwise.
Question 2: A cylinder and a cone have the same base radius and height. What is the ratio of the cylinder's volume to the cone's volume?
- 1:1
- 2:1
- 3:1 (Correct answer)
- 4:1
Correct answer: 3:1
The cylinder's volume is πr²h and the cone's is ⅓πr²h, so the ratio is 3:1.
Question 3: If you punch a hole through the center of a folded square piece of paper (folded once), how many holes appear when unfolded?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
One fold creates two layers, so one hole through both layers produces 2 holes when unfolded.
Question 4: A room is viewed from the left side. You see two windows side by side. Viewed from the right side, how do the windows appear?
- Still side by side in the same order
- Side by side but in reversed left-right order (Correct answer)
- One above the other
- Only one window is visible
Correct answer: Side by side but in reversed left-right order
Viewing from the opposite side mirrors the image, reversing the left-right order of the windows.
Question 5: A square is cut diagonally to create two pieces. Each piece is then arranged to form a new shape. What shape can they form?
- A circle
- A larger square
- A rectangle
- A triangle (Correct answer)
Correct answer: A triangle
Two right triangles from a diagonal cut can be arranged into a larger triangle.
Question 6: On a grid, point A is at (2, 3) and point B is at (5, 7). If both points move 3 units right and 2 units down, what are the new coordinates of A?
- (5, 1)
- (5, 5) (Correct answer)
- (−1, 5)
- (2, 3)
Correct answer: (5, 5)
Moving right adds to x and moving down subtracts from y: (2+3, 3−2) = (5, 1).
Question 7: Which net cannot fold into a cube?
- A cross of 6 squares
- A row of 4 squares with 1 above and 1 below the second
- A row of 4 squares with 2 attached to one side
- A straight row of 6 squares (Correct answer)
Correct answer: A straight row of 6 squares
A straight row of 6 squares cannot fold into a cube because opposite faces would overlap.
Basic Ability Test Basic Ability Spatial Reasoning and Visualization 4
A figure is rotated 270° clockwise.
This is equivalent to a rotation of how many degrees counterclockwise?