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GMAT Practice Question - Solid Geometry

Question 1

Medium Problem Solving Concepts Covered1. Surfaces of cubes. 1 concept

This GMAT quant practice question is from the topic Mensuration (Solid Geometry): Concept covered is properties of surfaces of cubes.

Solid Geometry
1
Cubes
A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
  1. 9
  2. 61
  3. 98
  4. 54
  5. 64
Correct Answer     Choice D. 54 cubes will have exactly one of their sides painted.

Explanatory Answer

When a 5 cc cube is sliced into 1 cc cubes, we will get 5 * 5 * 5 = 125 cubes of 1 cubic centimeter.

In each side of the larger cube, the smaller cubes on the edges will have more than one of their sides painted.
Therefore, the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted.

In each face of the larger cube, there will be 5 * 5 = 25 cubes.
Of these, the cubes on the outer rows will be on the edge. 16 such cubes exist on each face.
If we count out the two outer rows on either side of a face of the cube, we will be left with 3 * 3 = 9 cubes which are not on the edge in each face of the cube.
Therefore, there will be 9 cubes of 1-cc volume per face that will have exactly one of their sides painted.
In total, there will be 9 * 6 = 54 such cubes.

Choice D is the correct answer.

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