3 Tips on Cracking Reasoning Questions on Dice, Cubes and Cuboids

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Tip #1: Mentally rotate the dice to see which faces are adjacent and which are opposite

1.Question: Two positions of a dice are shown below. Which number will appear on the face opposite to the face with the number 4?          

Solution:                                           

2, 3, 5 and 6 are adjacent to 4 and cannot be opposite to 4. The current answer is 1.

2. Question: Two positions of a dice are shown below. Which number will appear on the face opposite to the face with the number 2?          

Solution:                                           

From the given figures, it is clear that figure (ii) is obtained by rotating the cube in figure (i) one face to the left while holding the top and bottom constant. Hence, the opposite face of 2 has 4.

3. Question: Two positions of a dice are shown below. Which number will appear on the face opposite to the face with the number 4?          

Solution:                                           

Figure (ii) is obtained by making two rotations from (i) while holding the front (face with 3) and back constant. Hence, the opposite of 4 is 2.

4. Question: Two positions of a dice are shown below. Which number will appear on the face opposite to the face with the number 3?          

Solution:                                           

If you mentally rotate cube in figure (i) such that face 1 goes to the right and 5 and 3 are hidden from view with 5 at the bottom and 3 at the back, you will arrive at (ii). Hence, the opposite of 3 is 2.

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Tip #2: While folding a plus into a cube, the square at the longer end always forms the top of the cube and the middle square at the intersection will be the base of the cube

Question: The figure given on the left hand side in each of the following questions is folded to form a box. Choose from the alternatives (1), (2), (3) and (4) the boxes that is similar to the box formed

A.   1, 2 and 4 only

B.    3 and 4 only

C.    1 and 2 only

D. 1, 2 and 3 only

Solution:

The square at the longer end will form the top while the middle square will form the base. The rest 4 sides that consist of 2 unshaded squares and 2 partially shaded squares will form the lateral edges. By rotating the dice formed, we would be able to visualize (1), (2) and (4). So, the correct option will be A.

Tip #3: Draw indicative diagrams for cubes and cuboids to simplify the problem

A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height. Two sides measuring 5 cm x 4 cm are colored in red. Two faces measuring 4 cm x 3 cm are colored in blue. Two faces measuring 5 cm x 3 cm are colored in green. Now the block is divided into small cubes of side 1 cm each.

Question: How many small cubes will have two faces colored with red and green colors? Other faces of the small cube could be colored or blank.

A. 12    B. 8           C. 16              D. 20

Solution:

Cubes painted red and green on two sides will be along the left and right sides (5 cm length each) of the top and the bottom face. Thus, no. of such cubes = 5 x 4 = 20. Answer is D.

Question: How many small cubes will have no faces colored?

A. None           B. 2               C. 4             D. 6

Solution:

The cubes that will not be part of the faces of the cuboid will have no color. Thus, no. of such cubes = 2 x 3 x 1 = 6. So the correct answer will be D.

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