JIPMAT 2024 (LR) - A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. Which of the following statements are correct?(A) The number of smaller cubes with two surfaces painted is 36.(B) The number of smaller cubes with one surface painted is 24.(C) The number of smaller cubes with no surface painted is 8.(D) The number of smaller cubes with at least two surfaces painted is 30. | PYQs + Solutions | AfterBoards
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JIPMAT 2024

Logical Reasoning
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Dices & Cubes

Medium

A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. Which of the following statements are correct?
(A) The number of smaller cubes with two surfaces painted is 36.
(B) The number of smaller cubes with one surface painted is 24.
(C) The number of smaller cubes with no surface painted is 8.
(D) The number of smaller cubes with at least two surfaces painted is 30.

Correct Option: 3
First, let's understand what we're working with: \newline The original cube is colored red on all faces, cut into 6464 smaller cubes, making it a 4×4×44 \times 4 \times 4 cube.
Let's analyze each type:
Cubes with three painted faces: \newline These are the corner pieces. Number of corners = 88 cubes
Cubes with two painted faces: \newline These are the edge pieces (but not corners). On a 4×4×44 \times 4 \times 4 cube, each edge has 22 cubes between corners. Number of edges = 1212. Total = 12×2=2412 \times 2 = 24 cubes
Cubes with one painted face: \newline These are center pieces on each face (not edges/corners). Each face is 4×44 \times 4 with interior 2×22 \times 2. Each face has 44 center pieces. With 66 faces, total = 6×4=246 \times 4 = 24 cubes
Cubes with no painted faces: \newline These are completely interior cubes, forming a 2×2×22 \times 2 \times 2 interior cube = 88 cubes
Let's check each statement: \newline (A) "Two surfaces painted = 3636" \newline False, it's 2424 cubes
(B) "One surface painted = 2424" \newline True
(C) "No surface painted = 88" \newline True
(D) "At least two surfaces painted = 3030" \newline False, it's 88 (three faces) + 2424 (two faces) = 3232 cubes
Therefore, only statements (B) and (C) are correct.

Related questions:

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This question is based on the information given below: The six faces of cube are painted in a manner that no two adjacent faces have the same colour. The three colours used in painting are red, blue and green. The cube is then cut into 36 smaller cubes in a manner that 32 cubes are of one size and the rest of a bigger size and each of the bigger cube has no red side. How many cubes only have one side coloured?

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A cube has six numbers marked 1,2,3,4,51,2,3,4,5 and 6 on its faces. Four views of the cube are shown below :
What is the number on the face opposite to the face showing 4 ?

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