Test: Cubes & Cuboids


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31 Questions MCQ Test Logical Reasoning (LR) and Data Interpretation (DI) | Test: Cubes & Cuboids

Test: Cubes & Cuboids for CAT 2022 is part of Logical Reasoning (LR) and Data Interpretation (DI) preparation. The Test: Cubes & Cuboids questions and answers have been prepared according to the CAT exam syllabus.The Test: Cubes & Cuboids MCQs are made for CAT 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Cubes & Cuboids below.
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Test: Cubes & Cuboids - Question 1

Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

Question -

How many cubes having red, green and black colours on at least one side of the cube will be formed ?

Detailed Solution for Test: Cubes & Cuboids - Question 1

Such cubes are related to the corners of the cuboid. Since the number of corners of the cuboid is 4.

Hence, the number of such small cubes is 4.

Test: Cubes & Cuboids - Question 2

Directions to Solve

The following questions are based on the information given below:

All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.

Question -

How many small cubes are there where one face is green and other one is either black or red ?

Detailed Solution for Test: Cubes & Cuboids - Question 2

Number of small cubes having one face green and the other one is either red or black = 8 x 2 = 16

Test: Cubes & Cuboids - Question 3

Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

Question -

How many small cubes will be formed ?

Detailed Solution for Test: Cubes & Cuboids - Question 3

Number of small cubes = l x b x h = 6 x 4 x 1 = 24

Test: Cubes & Cuboids - Question 4

Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

Question -

How many cubes will have 4 coloured sides and two non-coloured sides ?

Detailed Solution for Test: Cubes & Cuboids - Question 4

Only 4 cubes situated at the corners of the cuboid will have 4 coloured and 2 non-coloured sides.

Test: Cubes & Cuboids - Question 5

Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

Question -

How many cubes will remain if the cubes having black and green coloured are removed ?

Detailed Solution for Test: Cubes & Cuboids - Question 5

Number of small cubes which are Black and Green is 8 in all.

Hence, the number of remaining cubes are = 24 - 8 = 16

Test: Cubes & Cuboids - Question 6

Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

Question -

How many cubes will have green colour on two sides and rest of the four sides having no colour ?

Detailed Solution for Test: Cubes & Cuboids - Question 6

There are 16 small cubes attached to the outer walls of the cuboid.

Therefore remaining inner small cubes will be the cubes having two sides green coloured.

So the required number = 24 - 16 = 8

Test: Cubes & Cuboids - Question 7

Directions to Solve

The following questions are based on the information given below:

  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.

Question -

How many small cubes will have only two faces coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 7

Number of small cubes having only two faces coloured = 6 from the front + 6 from the back + 2 from the left + 2 from the right

= 16

Test: Cubes & Cuboids - Question 8

Directions to Solve

The following questions are based on the information given below:

  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.

Question -

How many small cubes have three faces coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 8

Such cubes are related to the corners of the cuboid and there are 8 corners.

Hence, the required number is 8.

Test: Cubes & Cuboids - Question 9

Directions to Solve

The following questions are based on the information given below:

  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.

Question -

How many small cubes will have no face coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 9

Number of small cubes have no face coloured = (4 - 2) x (3 - 2) = 2 x 1 = 2

Test: Cubes & Cuboids - Question 10

Directions to Solve

The following questions are based on the information given below:

  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.

Question -

How many small cubes will have only one face coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 10

Number of small cubes having only one face coloured = 2 x 2 + 2 x 2 + 2 x 1

= 4 + 4 + 2

= 10

Test: Cubes & Cuboids - Question 11

Directions to Solve

The following questions are based on the information given below:

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

Question -

How many small cubes will have will have three faces coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 11

Such cubes are related to the corners of the cuboid and in the cuboid there are 8 corners.

Hence, the required number of small cubes is 8.

Test: Cubes & Cuboids - Question 12

Directions to Solve

The following questions are based on the information given below:

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

Question -

How many small cubes will have only one face coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 12

2 from the front + 2 from the back + 3 from the left + 3 from the right + 6 from the top + 6 from the bottom = 22

Test: Cubes & Cuboids - Question 13

Directions to Solve

The following questions are based on the information given below:

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

Question -

How many small cubes will have no faces coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 13

Required number of small cubes = (5 - 2) x (4 - 2) x (3 - 2)

= 3 x 2 x 1

= 6

Test: Cubes & Cuboids - Question 14

Directions to Solve

The following questions are based on the information given below:

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

Question -

How many small cubes will have two faces coloured with red and green colours ?

Detailed Solution for Test: Cubes & Cuboids - Question 14

Required number of small cubes = 6 from the top and 6 from the bottom = 12

Test: Cubes & Cuboids - Question 15

Directions to Solve

The following questions are based on the information given below:

  1. All the faces of cubes are painted with red colour.
  2. The cubes is cut into 64 equal small cubes.

Question -

How many small cubes have only one face coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 15

Number of small cubes having only one face coloured = (x - 2)2 x No. of faces

= (4 - 2)2 x 6

= 24

Test: Cubes & Cuboids - Question 16

Directions to Solve

The following questions are based on the information given below:

  1. All the faces of cubes are painted with red colour.
  2. The cubes is cut into 64 equal small cubes.

Question -

How many small cubes have no faces coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 16

Number of small cubes having only one faces coloured = (x - 2)3

Here, x = side of big cube / side of small cube

x = 4 /1

x = 4

Required number = (4 -2)3

= 8

Test: Cubes & Cuboids - Question 17

Directions to Solve

The following questions are based on the information given below:

  1. All the faces of cubes are painted with red colour.
  2. The cubes is cut into 64 equal small cubes.

Question -

How many small cubes are there whose three faces are coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 17

Number of small cubes having three faces coloured = No. of corners = 8

Test: Cubes & Cuboids - Question 18

Directions to Solve

The following questions are based on the information given below:

  1. All the faces of cubes are painted with red colour.
  2. The cubes is cut into 64 equal small cubes.

Question -

How many small cubes are there whose two adjacent faces are coloured red ?

Detailed Solution for Test: Cubes & Cuboids - Question 18

Number of small cubes having two adjacent faces coloured red = (x - 2) x No. of edges

= (4 - 2) x 12

= 24

Test: Cubes & Cuboids - Question 19

Directions to Solve

The following questions are based on the information given below:

All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.

Question -

How many small cubes are there whose no faces are coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 19

Number of small cubes having no face coloured = (x - 2)3

= (4 - 2)3

= 8

Test: Cubes & Cuboids - Question 20

Directions to Solve

The following questions are based on the information given below:

All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.

Question -

How many small cubes are there whose 3 faces are coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 20

Number of small cubes having three faces coloured = 1 at each corner

= 1 x 8

= 8

>

Test: Cubes & Cuboids - Question 21

Directions to Solve

The following questions are based on the information given below:

All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.

Question -

How many small cubes are there whose only one face is coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 21

Number of small cubes having only one face coloured = 4 from each face

= 4 x 6

= 24

Test: Cubes & Cuboids - Question 22

Directions to Solve

The following questions are based on the information given below:

All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.

Question -

How many small cubes are there whose at the most two faces are coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 22

Number of small cubes having two faces coloured = 8 + 8 + 4 + 4 = 24

and Number of small cubes having only one face coloured = 4 x 6 = 24

and Number of small cubes having no face coloured = 4 + 4 = 8

Therefore, total number of small cubes whose at the most two faces are coloured = 24 + 24 + 8 = 56.

Test: Cubes & Cuboids - Question 23

Directions to Solve

All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes.

Question -

How many small cubes will be formed having only one face coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 23

No. of small cubes having only one face coloured = (5 - 2)2 x 6

= 9 x 6

= 54

Test: Cubes & Cuboids - Question 24

Directions to Solve

All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes.

Question -

How many small cubes will be formed having no face coloured ?

Detailed Solution for Test: Cubes & Cuboids - Question 24

No. of small cubes having no face coloured = (x - 2)3

= (5 - 2)3

= 27

Test: Cubes & Cuboids - Question 25

Directions to Solve

All the six faces of a cube of a cube are coloured with six different colours - black, brown, green, red, white and blue.

  1. Red face is opposite to the black face.
  2. Green face is between red and black faces.
  3. Blue face is adjacent to white face.
  4. Brown face is adjacent to blue face.
  5. Red face is in the bottom.

Question -

The upper face is _________

Detailed Solution for Test: Cubes & Cuboids - Question 25

Test: Cubes & Cuboids - Question 26

Directions to Solve

All the six faces of a cube of a cube are coloured with six different colours - black, brown, green, red, white and blue.

  1. Red face is opposite to the black face.
  2. Green face is between red and black faces.
  3. Blue face is adjacent to white face.
  4. Brown face is adjacent to blue face.
  5. Red face is in the bottom.

Question -

Which of the following is adjacent to green ?

Detailed Solution for Test: Cubes & Cuboids - Question 26

Test: Cubes & Cuboids - Question 27

Directions to Solve

All the six faces of a cube of a cube are coloured with six different colours - black, brown, green, red, white and blue.

  1. Red face is opposite to the black face.
  2. Green face is between red and black faces.
  3. Blue face is adjacent to white face.
  4. Brown face is adjacent to blue face.
  5. Red face is in the bottom.

Question -

Which face is opposite to green ?

Detailed Solution for Test: Cubes & Cuboids - Question 27

Test: Cubes & Cuboids - Question 28

Directions to Solve

There are 128 cubes with me which are coloured according to two schemes viz.

  1. 64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.
  2. 64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up.

Question -

How many cubes have at least two coloured red faces each ?

Detailed Solution for Test: Cubes & Cuboids - Question 28

64 and 64 cubes of both types of cubes are such who have at least two coloured faces red each.

Therefore, total number of the required cubes is 128.

Test: Cubes & Cuboids - Question 29

Directions to Solve

There are 128 cubes with me which are coloured according to two schemes viz.

  1. 64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.
  2. 64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up.

Question -

What is the total number of red faces ?

Detailed Solution for Test: Cubes & Cuboids - Question 29

No. of red faces among first 64 cubes = 128

No. of red faces among second 64 cubes = 192

Therefore, total number of red faces = 128 + 192 = 320

Test: Cubes & Cuboids - Question 30

Directions to Solve

There are 128 cubes with me which are coloured according to two schemes viz.

  1. 64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.
  2. 64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up.

Question -

Which two colours have the same number of faces ?

Detailed Solution for Test: Cubes & Cuboids - Question 30

First 64 cubes are such each of whose two faces are green and second 64 cubes are such each of whose two faces are blue.

Therefore, green and blue colours have the same number of faces.

Test: Cubes & Cuboids - Question 31

Directions to Solve

There are 128 cubes with me which are coloured according to two schemes viz.

  1. 64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.
  2. 64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up.

Question -

How many cubes have two adjacent blue faces each ?

Detailed Solution for Test: Cubes & Cuboids - Question 31

Second 64 cubes are such each of whose two faces are blue.

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