Logical Reasoning

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.

(A), (B) and (D) only

(B), (C) and (D) only

(B) and (C) only

(A) and (D) only

✅ Correct Option: 3

First, let's understand what we're working with:

The original cube is colored red on all faces, cut into $64$ smaller cubes, making it a $4 \times 4 \times 4$ cube.

Let's analyze each type:

Cubes with three painted faces:

These are the corner pieces. Number of corners = $8$ cubes

Cubes with two painted faces:

These are the edge pieces (but not corners). On a $4 \times 4 \times 4$ cube, each edge has $2$ cubes between corners. Number of edges = $12$ . Total = $12 \times 2 = 24$ cubes

Cubes with one painted face:

These are center pieces on each face (not edges/corners). Each face is $4 \times 4$ with interior $2 \times 2$ . Each face has $4$ center pieces. With $6$ faces, total = $6 \times 4 = 24$ cubes

Cubes with no painted faces:

These are completely interior cubes, forming a $2 \times 2 \times 2$ interior cube = $8$ cubes

Let's check each statement:

(A) "Two surfaces painted = $36$ "

False, it's $24$ cubes

(B) "One surface painted = $24$ "

True

(D) "At least two surfaces painted = $30$ "

False, it's $8$ (three faces) + $24$ (two faces) = $32$ cubes

Therefore, only statements (B) and (C) are correct.

JIPMAT 2021

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?

JIPMAT 2025

If four different positions of a dice are shown below

then what number is opposite 3?

JIPMAT 2025

If a cube is painted yellow on all faces and cut into 27 small cubes of equal size, then which of the following are correct?

A. Six cubes are painted on one face only.

B. There is only one cube which is not painted on any face.

C. There are six cubes which have two faces painted.

D. There are eight cubes which have three faces painted.

JIPMAT 2026

If a cube is coloured red on all faces and cut into 64 smaller cubes of equal size, then which of the following are correct?

A. Sixteen small cubes have no face coloured.

B. Twenty four small cubes have only one face coloured.

C. None of the cubes can have its opposite faces coloured red.

D. There are eight cubes which have three faces coloured.

JIPMAT 2026

Three different positions of same dice are given below.

The number opposite to the number 2 is:

Solution

Related questions:

Keyboard Shortcuts

JIPMAT Past Year Questions (Topic-Wise)