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Test Level 1: Cubes & Dices - CAT MCQ


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10 Questions MCQ Test Level-wise Tests for CAT - Test Level 1: Cubes & Dices

Test Level 1: Cubes & Dices for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 1: Cubes & Dices questions and answers have been prepared according to the CAT exam syllabus.The Test Level 1: Cubes & Dices MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 1: Cubes & Dices below.
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Test Level 1: Cubes & Dices - Question 1

Directions: Read the following information and answer the given question.

A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes obtained are now separated.

Q. How many smaller cubes have no coloured face?

Detailed Solution for Test Level 1: Cubes & Dices - Question 1

Number of smaller cubes with no face coloured = (n – 2)3 = (4 – 2)3 = 8

Test Level 1: Cubes & Dices - Question 2

Directions: Read the following information and answer the given question.

A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes so obtained are now separated.

Q. How many smaller cubes have only two surfaces painted with red colour?

Detailed Solution for Test Level 1: Cubes & Dices - Question 2

Number of smaller cubes with two surfaces painted red = (n – 2) × 12 = (4 – 2) × 12 = 24

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Test Level 1: Cubes & Dices - Question 3

Directions: One hundred and twenty five cubes of the same size are arranged in the form of a cube on a table. Then, a column of five cubes is removed from each of the four corners. All the exposed faces of the rest of the solid (except the face touching the table) are coloured red. Now, answer the question based on the above statements.

Q. How many small cubes are there in the solid after the removal of the columns?

Detailed Solution for Test Level 1: Cubes & Dices - Question 3


Since out of 125 total number of cubes, we removed 4 columns of 5 cubes each, the remaining number of cubes = 125 – (4 × 5) = 125 – 20 = 105

Test Level 1: Cubes & Dices - Question 4

Directions: Read the following information and answer the given question.

One hundred and twenty five cubes of the same size are arranged in the form of a cube on a table. Then, a column of five cubes is removed from each of the four corners. All the exposed faces of the rest of the solid (except the face touching the table) are coloured red.

Q. How many cubes have only one red face?

Detailed Solution for Test Level 1: Cubes & Dices - Question 4


There are 9 + (4 × 4) = 25 such cubes

Test Level 1: Cubes & Dices - Question 5

Directions: Read the following information and answer the given question.

A cube is painted red on two adjacent surfaces, black on the surface opposite to the red surfaces and green on the remaining faces. Now, the cube is cut into 64 smaller cubes of equal size.

Q. How many smaller cubes have only one surface painted?

Detailed Solution for Test Level 1: Cubes & Dices - Question 5

Since the surfaces of the big cube are painted with some colours, so the number of smaller cubes with only one surface painted is (n – 2) × 12 = (4 – 2) × 12 = 2 × 12 = 24.

Test Level 1: Cubes & Dices - Question 6

Two orientations of a die are shown below. When number 2 is on the top, then which number is at the bottom?

Detailed Solution for Test Level 1: Cubes & Dices - Question 6

From figures (i) and (ii), we conclude that numbers 1, 5, 6 and 3 appear adjacent to number 2.
Therefore, number 2 must appear opposite to number 4.
Thus, if number 2 is on the top, then number 4 is at the bottom.

Test Level 1: Cubes & Dices - Question 7

Two orientations of a dice are shown below. If the face with 1 dot is at the bottom, then how many dots will be at the top of the dice?

Detailed Solution for Test Level 1: Cubes & Dices - Question 7

From figures (i) and (ii), we conclude that 5, 4, 6 and 2 dots appear adjacent to 3 dots.
Therefore, 1 dot must appear opposite to 3 dots.
Thus, if the face with 1 dot is at the bottom, then the face with 3 dots will appear at the top.

Test Level 1: Cubes & Dices - Question 8

Two orientations of a block are shown below:

Q. When six is at the bottom, which number will be at the top?

Detailed Solution for Test Level 1: Cubes & Dices - Question 8

From figures (i) and (ii), we conclude that the numbers 1, 2, 3 and 4 appear adjacent to 6.
Thus, the number 5 will appear opposite 6.
Therefore, when 6 is at the bottom, then 5 will be at the top.

Test Level 1: Cubes & Dices - Question 9

In the given dice, a, b, c and d are written on the adjacent faces in a clockwise order, and e and f at the top and the bottom, respectively. When c is at the top, what will be at the bottom?

Detailed Solution for Test Level 1: Cubes & Dices - Question 9

Clearly, the six faces of the dice are labelled as shown:
Face I → a, Face II → b, Face III → c, Face IV → d, Face V → e, Face VI → f
Therefore, ‘a’ appears opposite ‘c’.
Hence, when ‘c’ is at the top, then ‘a’ will be at the bottom.

Test Level 1: Cubes & Dices - Question 10

Directions: Six dice are shown in the following figure, the upper faces of each dice having been erased. The number of dots on each surface of every dice has been arranged in such a way that the sum of the number of dots on the opposite faces is 7.

sum of the numbers on the top of first 3 dice

Detailed Solution for Test Level 1: Cubes & Dices - Question 10

According to the given figures,
Top face in (i) dice contain 3 dots;
Top face in (ii) dice contain 1 dots;
Top face in (iii) dice contain 3 dots;
Therefore,
Total dots = 3 + 1 + 3 = 7
Correct Answer: 7

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