Free GMA Spatial Reasoning Questions and Answers 1 — Questions and Answers
Question 1: A flat pattern is shown, which can be folded into a cube. Which of the options represents a possible view of the folded cube? The pattern is: Top face is a circle. Middle row from left to right: square, star, triangle. Bottom face (below the star) is a plus sign.
- A cube showing the star on the front, the square on the right, and the circle on top.
- A cube showing the star on the front, the triangle on the right, and the circle on top. (Correct answer)
- A cube showing the circle on the front and the plus sign on the top.
- A cube showing the square on the front and the triangle on the back.
Correct answer: A cube showing the star on the front, the triangle on the right, and the circle on top.
When the net is folded, the star is the front face. The square is on the left, the triangle is on the right, the circle is on top, and the plus sign is on the bottom. The only option that correctly shows the relative positions of the star (front), triangle (right), and circle (top) is the correct one.
Question 2: Which of the options is a rotation of the 3D figure shown? The figure is an 'L' shape made of four cubes, with a fifth cube attached to the top of the corner cube.
- A figure where the fifth cube is attached to the end of the 'L' instead of the corner.
- A mirror image of the original figure.
- The original figure rotated 90 degrees clockwise on its vertical axis. (Correct answer)
- A figure where the 'L' shape is made of five cubes instead of four.
Correct answer: The original figure rotated 90 degrees clockwise on its vertical axis.
The correct answer is the only figure that maintains the exact same structure and arrangement of cubes as the original, merely viewed from a different angle. The incorrect options are either mirror images or have cubes moved to different positions, altering the fundamental shape.
Question 3: Given the unfolded cube pattern, which cube could be formed? The pattern has a horizontal row of four faces (2, 3, 4, 5), with face 1 above face 3, and face 6 below face 3.
- A cube showing faces 1, 3, and 6.
- A cube showing faces 2, 3, and 4.
- A cube showing faces 1, 2, and 3. (Correct answer)
- A cube showing faces 3, 5, and 6.
Correct answer: A cube showing faces 1, 2, and 3.
In this T-shaped net, face 3 is central. Faces 2 and 4 are opposite, faces 1 and 6 are opposite, and faces 3 and 5 are opposite. The correct option shows three faces (1, 2, 3) that can all be adjacent to each other when folded.
Question 4: Which of the options is a simple rotation of the main figure? The figure consists of a 2x2 base of cubes with one cube removed from a corner, and a single cube placed on top of the cube diagonal to the empty space.
- The figure rotated 180 degrees around the vertical axis. (Correct answer)
- A mirror image of the figure.
- A figure where the top cube is above the empty space.
- A figure with a complete 2x2 base.
Correct answer: The figure rotated 180 degrees around the vertical axis.
The correct answer is the only option that preserves the spatial relationship between all the component cubes. It is the same object, just turned in space. The other options alter the structure, for example, by moving the top cube or creating a mirror image.
Question 5: A cube net has the following faces: Top: horizontal stripes. Middle row: dots, solid black, checkerboard. Bottom: vertical stripes. Which is a valid folded cube?
- A cube showing the solid black front, checkerboard right, and vertical stripes top.
- A cube showing the dots front, and the checkerboard top.
- A cube showing the solid black front, checkerboard right, and horizontal stripes top. (Correct answer)
- A cube showing the horizontal stripes front, and the vertical stripes top.
Correct answer: A cube showing the solid black front, checkerboard right, and horizontal stripes top.
When folded, the solid black face can be the front. This places the dots on the left, the checkerboard on the right, and the horizontal stripes on top. The orientation of the stripes is crucial; they must remain horizontal relative to the upright solid face.
Question 6: Which of the four options is a rotation of the target 3D object, which is a rectangular block with one corner cut off at an angle?
- The object with the opposite corner cut off.
- The object rotated so the cut face is on the bottom-left. (Correct answer)
- The object with a whole edge cut off, not just a corner.
- A mirror image of the object.
Correct answer: The object rotated so the cut face is on the bottom-left.
The correct answer is the only option that is structurally identical to the target object. The other options are incorrect because they are either mirror images (a different corner is cut) or the cut is made on an edge instead of a corner, fundamentally changing the shape.
Free GMA Spatial Reasoning Questions and Answers 1
A flat pattern is shown, which can be folded into a cube.
Which of the options represents a possible view of the folded cube? The pattern is: Top face is a circle.
Middle row from left to right: square, star, triangle.
Bottom face (below the star) is a plus sign.