What is the volume of a certain cube?

For this question, you need to know:
1) A cube has 12 equal length sides, so sum of side length = 12 (length of one side)
2) surface area of a square = length x width (since length = width in a square) = length x length
3) A cube has 6 square faces with equal area, so sum of surface area = 6 (surface area of one side) = 6 (length x length)
4) volume of a cube = length x length x length

So, let's start with statement 1:

Sum of lengths = 36 = 12 (length of one side)
Using algebra, you know that length of one side = 3
Once you have length of one side, you know the volume of the cube. Therefore this is SUFFICIENT.

Eliminate B, C and E.

On to statement 2:
Total surface area = 54
Since there are 6 square faces: 54/6 = area for 1 face = 9
Since area of 1 face of square = 9 = length x length = 3x3
Length of one side = 3
Once you have length of one side, you know the volume of the cube. Therefore this is SUFFICIENT.

Correct answer D.

All you need to uniquely define a cube is any one measurement - length of a side/edge, area of a surface, volume etc. If you have any one of them, you can uniquely determine the others. So each statement alone is sufficient here.

To show how,

(1) The sum of the lengths of the edges of the cube is 36.
A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3
Volume = 3*3*3 = 27

(2) The surface area of the cube is 54.
A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)
6s^2 = 54
s = 3
Volume = 3*3*3 = 27

Answer (D)
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we have find volume of the cube

Statement 1 gives information about sum of lengths of all sides of a cube
we know that cube has 12 sides (edges) so each side = 36/12 = 3
Volume of cube = 27
So sufficient

Statement 2 gives the information about the total surface area of the cube = 54
we know that cube has 6 equal faces area of single face = 9 which in turn gives us the side as 3
Volume of cube = 27
So sufficient

Correct Answer - D

Volume of a cube = side^3

Statement 1: 6x = 36. x = 6. Volume = 6^3.
Sufficient.

Statement 2: 6x^2 = 54. x = 3. Volume = 3^3
Sufficient.

D.

However, the two answers are contradictory, which doesn't happen on GMAT.

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