GCAT - General Cognitive Ability Spatial Visualization Tasks Questions and Answers — Questions and Answers
Question 1: An unfolded cardboard cube is shown with symbols on four of its faces. The net shows a horizontal row of four squares and two additional squares, one attached above and one below the second square in the row. From left to right, the symbols on the horizontal row are: blank, plus sign, arrow pointing right, blank. The square above the plus sign has a circle. The square below the plus sign has a triangle. Which of the following 3D cubes can be formed from this net?
- A cube showing the plus sign on the front, the right-pointing arrow on the right face, and the circle on the top face. (Correct answer)
- A cube showing the plus sign on the front, the triangle on the right face, and the circle on the top face.
- A cube showing the right-pointing arrow on the front, the plus sign on the right face, and the triangle on the top face.
- A cube showing the circle on the front, the triangle on the bottom, and the plus sign on the back.
Correct answer: A cube showing the plus sign on the front, the right-pointing arrow on the right face, and the circle on the top face.
When the net is folded, the circle becomes the top face, the triangle becomes the bottom face, and the plus sign becomes the front face. Consequently, the square with the right-pointing arrow must be the right-side face. The other options show incorrect adjacency or orientation of the faces.
Question 2: A 3D object is composed of stacked cubes. The front view shows a 2x2 square of cubes. The right-side view shows a column of two cubes on the left and a single cube on the right. Which of the following is the correct top-down view of the object?
- A 2x2 square with the bottom-right quadrant empty. (Correct answer)
- A 2x2 square with the top-left quadrant empty.
- A 2x2 square with all quadrants filled.
- A 2x2 square with the bottom-left quadrant empty.
Correct answer: A 2x2 square with the bottom-right quadrant empty.
The front view establishes a 2x2 footprint with at least one cube in each column. The right-side view shows that the back column is two cubes high and the front column is one cube high. This means from the top, you would see the two cubes in the back row and only one in the front row. The single cube in the front row corresponds to the single cube seen from the right-side view, meaning the bottom-right position (front-right from a top view) is empty. Therefore, the object consists of three cubes in an 'L' shape when viewed from the top.
Question 3: An irregular L-shaped figure has a long vertical arm and a shorter horizontal arm extending to the right. Which of the following figures represents a mental rotation of the original figure, and not a reflection?
- An L-shaped figure with a long horizontal arm extending to the right and a shorter vertical arm pointing down.
- An L-shaped figure with a long vertical arm and a shorter horizontal arm extending to the left.
- An L-shaped figure with a long horizontal arm extending to the left and a shorter vertical arm pointing down.
- An L-shaped figure with a long vertical arm pointing down and a shorter horizontal arm extending to the right. (Correct answer)
Correct answer: An L-shaped figure with a long vertical arm pointing down and a shorter horizontal arm extending to the right.
Mental rotation involves turning the object in 2D space without flipping it over. Option D is the original figure rotated 180 degrees. Option B is a mirror image (reflection) of the original shape, not a rotation. Options A and C are both reflections and rotations.
Question 4: A square piece of paper is folded in half diagonally from the top-right corner to the bottom-left corner. Then, the resulting triangle is folded in half again along its line of symmetry. A small circular hole is punched through the center of this final, smaller triangle. What will the paper look like when fully unfolded?
- A square with one hole in the center.
- A square with two holes along the main diagonal. (Correct answer)
- A square with four holes forming a smaller square in the center.
- A square with four holes along the main diagonal.
Correct answer: A square with two holes along the main diagonal.
The first unfold is along the triangle's line of symmetry. This mirrors the single hole, creating two holes in the larger triangle. The second unfold is along the diagonal of the original square. This mirrors the two holes across that diagonal, but since the holes are located on the fold line itself, they do not duplicate. The result is two holes positioned on the diagonal that was used for the first fold.
Question 5: An isometric view of a structure made of identical cubes is shown. The structure has a base of three cubes in a row. A second layer of two cubes sits on top of the rightmost two cubes of the base. A single cube sits on top of the rightmost cube of the second layer. How many cubes are in the structure in total, including those hidden from view?
- A. 10
- B. 5
- C. 6 (Correct answer)
- D. 7
Correct answer: C. 6
To solve this, count the cubes layer by layer or column by column. The base layer has 3 cubes. The second layer, which requires the base layer for support, has 2 cubes. The top layer has 1 cube. The total number of cubes is the sum of the cubes in each layer: 3 + 2 + 1 = 6 cubes.
Question 6: You are given three separate 2D shapes: two identical right-angled triangles and one small square. The length of the two shorter sides of the triangles is equal to the side length of the square. Which of the following composite shapes can be formed by fitting these three pieces together without any overlap?
- A larger square.
- A regular pentagon.
- A parallelogram. (Correct answer)
- A larger right-angled triangle.
Correct answer: A parallelogram.
The two right-angled triangles can be joined along their hypotenuses to form a rectangle that is twice as long as it is wide. However, to use all three pieces, you can place the two triangles together along one of their shorter sides to form a larger triangle. Then, place the square adjacent to the combined side. A more direct assembly is to place the hypotenuse of each triangle against opposite sides of the square, forming a parallelogram.
GCAT - General Cognitive Ability Spatial Visualization Tasks Questions and Answers
An unfolded cardboard cube is shown with symbols on four of its faces.
The net shows a horizontal row of four squares and two additional squares, one attached above and one below the second square in the row.
From left to right, the symbols on the horizontal row are: blank, plus sign, arrow pointing right, blank.
The square above the plus sign has a circle.
The square below the plus sign has a triangle.
Which of the following 3D cubes can be formed from this net?