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Cubes || Logical reasoning || CAT 2021 || 29 May

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Question 1

Directions: These questions are based on the following information.

A cube of
Description: E:\CAT\SNAP\SNAP-2011-Solution_files\image001.png is kept in the corner of a room and painted in three different colours, each face in one colour. The cube is cut into 343 smaller but identical cubes.
How many smaller cubes do not have any face painted?

Question 2

Directions: These questions are based on the following information.

A cube of
Description: E:\CAT\SNAP\SNAP-2011-Solution_files\image001.png is kept in the corner of a room and painted in three different colours, each face in one colour. The cube is cut into 343 smaller but identical cubes.
How many smaller cubes have exactly one colour on them?

Question 3

Directions: These questions are based on the following information.

A cube of
Description: E:\CAT\SNAP\SNAP-2011-Solution_files\image001.png is kept in the corner of a room and painted in three different colours, each face in one colour. The cube is cut into 343 smaller but identical cubes.
How many smaller cubes have at the most two faces painted?

Question 4

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

Question 5

How many cubes of dimensions 1cm x 1cm x 1cm are required to cover a cube of dimensions 7 cm x 7 cm x 7 cm?

Question 6

Directions: A cube is painted in such a way that a pair of adjacent faces is painted in green, a pair of opposite faces is painted in yellow and another pair of adjacent faces is painted in red. This cube is now cut into 125 identical cubes.
How many small cubes have exactly 2 faces painted in green?

Question 7

Directions: A cube is painted in such a way that a pair of adjacent faces is painted in green, a pair of opposite faces is painted in yellow and another pair of adjacent faces is painted in red. This cube is now cut into 125 identical cubes.
How many small cubes have at least two different colours on their faces?

Question 8

Directions: A cube is painted in such a way that a pair of adjacent faces is painted in green, a pair of opposite faces is painted in yellow and another pair of adjacent faces is painted in red. This cube is now cut into 125 identical cubes.
How many of the small cubes have exactly one colour on them?

Question 9

Directions: A cube is painted in such a way that a pair of adjacent faces is painted in green, a pair of opposite faces is painted in yellow and another pair of adjacent faces is painted in red. This cube is now cut into 125 identical cubes.
How many of the small cubes do not have green colour but have yellow or red on them?

Question 10

Directions: A cube is painted in such a way that a pair of adjacent faces is painted in green, a pair of opposite faces is painted in yellow and another pair of adjacent faces is painted in red. This cube is now cut into 125 identical cubes.
How many small cubes have exactly two painted faces and have exactly two colours on them?
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May 29CAT & MBA