GRE Math Challenge Question #26:
Quantity A
After selecting one vertex of the cube, the number of straight line segments longer than 4 that can be drawn from that vertex of the cube to another vertex of the cube
Quantity B
When the cube is placed on a flat surface, the maximum number of edges of the cube that can be touching the flat surface at once
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Explanation:
If a cube has side length of 4, all of the “straight line segments” connecting vertices of the cube along an edge of the cube will have length of 4. The only straight line segments between vertices that are longer than 4 are those that go diagonally through the cube or diagonally across a face.
From a selected vertex of the cube, there are 3 diagonals across the adjacent faces of the cube, and 1 diagonal through the cube to the opposite vertex.
Thus, Quantity A is 4.
Correct Choice: C (The two quantities are equal.)
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