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Practice set - 2 || Logical Reasoning || CAT 2021 || 29 April (App update required to attempt this test)

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Question 1

Direction: Read the paragraph carefully and answer the questions:

729 small cubelets are painted green on each face and then arranged together so as to form 27 identical medium-sized cubes. Each of these 27 medium-sized cubes is painted black on all the outside faces. The 27 medium-sized cubes are now arranged to form one large cube and the faces of this large cube are painted green again.

What is the number of small cubelets that have at least one face painted black?

Question 2

Direction: Read the paragraph carefully and answer the questions:

729 small cubelets are painted green on each face and then arranged together so as to form 27 identical medium-sized cubes. Each of these 27 medium-sized cubes is painted black on all the outside faces. The 27 medium-sized cubes are now arranged to form one large cube and the faces of this large cube are painted green again.

What is the number of small cubelets that have at least one face painted green?

Question 3

Direction: Read the paragraph carefully and answer the questions:

729 small cubelets are painted green on each face and then arranged together so as to form 27 identical medium-sized cubes. Each of these 27 medium-sized cubes is painted black on all the outside faces. The 27 medium-sized cubes are now arranged to form one large cube and the faces of this large cube are painted green again.

What is the number of small cubelets which have an equal number of faces painted green and black?

Question 4

Direction: Read the paragraph carefully and answer the questions:

729 small cubelets are painted green on each face and then arranged together so as to form 27 identical medium-sized cubes. Each of these 27 medium-sized cubes is painted black on all the outside faces. The 27 medium-sized cubes are now arranged to form one large cube and the faces of this large cube are painted green again.

What is the number of small cubelets that have all the faces painted green?

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.

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

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.

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

Question 7

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 8

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 9

What is the maximum possible number of identical pieces of cubes that can be cut into by 8 cuts?

Question 10

In the figures given below, two positions of a cubical block are shown. When 5 is at the top which number will be at bottom?
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Apr 29CAT & MBA