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# Cubes || Logical Reasoning || CAT 2021 || 12 October

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Question 1

The six faces of a wooden cube of side 6 cm are labelled A, B, C, D, E and F respectively. Three of these faces A, B, and C are each adjacent to the other two, and are painted red. The other three faces are not painted. Then, the wooden cube is neatly cut into 216 little cubes of equal size. How many of the little cubes have no sides painted?

Question 2

125 small but identical cubes have been put together to form a large cube. How many such small cubes will be required to cover this large cube completely?

Question 3

Direction:

A container in a shape of a cube, is used for mixing paints in factory. On each face of the container, a code, in a form of two digit number, is written. The paints that need mixing are injected into the container through a small hole, which is then sealed. The container is then placed in a machine which grips the top and bottom faces of the container and spins the container a few times from left to right, stopping intermittently. In the second Round of mixing, the container is removed and fixed again in the machine such that the top and bottom faces are different from the previous Round. The machine again spins the container from left to right, stopping intermittently. Many such Rounds are of mixing happens until paints are thoroughly mixed.

Dave was observing this process from the factory floor and, in each Round, whenever the machine stopped spinning the container, he noted down the code written on each one of the faces of the container that was visible to him. During any Round, the top and bottom faces of the container are not visible to Dave.

The following table provides the number that he noted down during different Rounds of mixing.

What is the code on the face which is opposite the face which has a code of 81?

Question 4

Direction:

A container in a shape of a cube, is used for mixing paints in factory. On each face of the container, a code, in a form of two digit number, is written. The paints that need mixing are injected into the container through a small hole, which is then sealed. The container is then placed in a machine which grips the top and bottom faces of the container and spins the container a few times from left to right, stopping intermittently. In the second Round of mixing, the container is removed and fixed again in the machine such that the top and bottom faces are different from the previous Round. The machine again spins the container from left to right, stopping intermittently. Many such Rounds are of mixing happens until paints are thoroughly mixed.

Dave was observing this process from the factory floor and, in each Round, whenever the machine stopped spinning the container, he noted down the code written on each one of the faces of the container that was visible to him. During any Round, the top and bottom faces of the container are not visible to Dave.

The following table provides the number that he noted down during different Rounds of mixing.

Which of the following pairs of codes are on faces which are opposite each other?

Question 5

Direction:

A container in a shape of a cube, is used for mixing paints in factory. On each face of the container, a code, in a form of two digit number, is written. The paints that need mixing are injected into the container through a small hole, which is then sealed. The container is then placed in a machine which grips the top and bottom faces of the container and spins the container a few times from left to right, stopping intermittently. In the second Round of mixing, the container is removed and fixed again in the machine such that the top and bottom faces are different from the previous Round. The machine again spins the container from left to right, stopping intermittently. Many such Rounds are of mixing happens until paints are thoroughly mixed.

Dave was observing this process from the factory floor and, in each Round, whenever the machine stopped spinning the container, he noted down the code written on each one of the faces of the container that was visible to him. During any Round, the top and bottom faces of the container are not visible to Dave.

The following table provides the number that he noted down during different Rounds of mixing.

In how many ways could the codes on the faces of the container have been written?

Question 6

Direction:

A container in a shape of a cube, is used for mixing paints in factory. On each face of the container, a code, in a form of two digit number, is written. The paints that need mixing are injected into the container through a small hole, which is then sealed. The container is then placed in a machine which grips the top and bottom faces of the container and spins the container a few times from left to right, stopping intermittently. In the second Round of mixing, the container is removed and fixed again in the machine such that the top and bottom faces are different from the previous Round. The machine again spins the container from left to right, stopping intermittently. Many such Rounds are of mixing happens until paints are thoroughly mixed.

Dave was observing this process from the factory floor and, in each Round, whenever the machine stopped spinning the container, he noted down the code written on each one of the faces of the container that was visible to him. During any Round, the top and bottom faces of the container are not visible to Dave.

The following table provides the number that he noted down during different Rounds of mixing.

What is the maximum possible sum of the codes on any two faces adjacent to each other?

Question 7

Answer the following questions based on the information given below.

I. There is a rectangular wooden block of length 4 cm, height 3 cm and breadth 3 cm.
II. The two opposite surfaces of are painted yellow on the outside.
III. The other two opposite surfaces of are painted red on the outside.
IV. The remaining two surfaces of are painted green on the outside.
V. Now, the block is cut in such a way that cubes of are created.
How many cubes will have only one colour?

Question 8

Answer the following questions based on the information given below.

I. There is a rectangular wooden block of length 4 cm, height 3 cm and breadth 3 cm.
II. The two opposite surfaces of are painted yellow on the outside.
III. The other two opposite surfaces of are painted red on the outside.
IV. The remaining two surfaces of are painted green on the outside.
V. Now, the block is cut in such a way that cubes of are created.
How many cubes will have no colour?

Question 9

Answer the following questions based on the information given below.

I. There is a rectangular wooden block of length 4 cm, height 3 cm and breadth 3 cm.
II. The two opposite surfaces of are painted yellow on the outside.
III. The other two opposite surfaces of are painted red on the outside.
IV. The remaining two surfaces of are painted green on the outside.
V. Now, the block is cut in such a way that cubes of are created.
How many cubes will have any two colours?

Question 10

1000 smaller cubes of dimensions 1cm x 1cm x 1cm are stacked together to form a large cube and then the cube is cut along a diagonal. How many of the smaller cubes are cut into two pieces?
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