A Cube Of Side 7 cm Is Coloured On Pair of Opposite Faces By Red, Green and Yellow Shades GMAT Problem Solving

Question: A cube of side 7 cm is coloured on pair of opposite faces by Red, Green and Yellow shades. The cube is then cut into unit cubes. How many of the unit cubes will have exactly two coloured faces?

1. 150
2. 125
3. 60
4. 49
5. 40

“A cube of side 7 cm is coloured on pair of opposite faces by Red, Green and Yellow shades.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

Let us look at the image below.

Only the edge cubes marked with dots will have exactly two colored faces.
A cube has 12 edges in total.
There are:

• 4 edges on the top square
• 4 on the bottom square
• 4 more that connect the 2 squares.

We get 5 cubes per edge.
There are a total of 12 edges.
Hence,
5 cubes per edge * 12 edges = 60 cubes

Correct Answer: C

Approach Solution 2:
Total edges in cube = 12
The corner most cubes on an edge have three faces painted. So out of all cubes on edges, take the 2 cubes out.
Since its side is 7cm and it is cut into a unit cube that means there are 7 cubes on 1 edge and we will take 2 cubes out: 7 - 2 = 5.
Total cubes with 2 face painted = 12 * 5 = 60

Correct Answer: C

Approach Solution 3:

12 edges total in a cube.
Three sides of the cubes on an edge's corner are painted. Take the two cubes out of all the cubes that are on the edges.
We will remove 2 cubes since its side is 7 cm and it was cut into a unit cube, which implies there are 7 cubes on 1 edge: 7 - 2 = 5.
12 * 5 = 60 total cubes with two faces painted.

Correct Answer: C

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