Let x be side of the cube.
1) The total surface area of cube = 6*x^2 =we can use this get x and the volume
2) diagonal connecting opposite corner =x*sqrt(3) =(sqrt(x^2+(xsqrt(2))^2))= 5 sqrt(3) we can use this get x and the volume

answer>> D

The correct answer is D. If we have one side of a cube, we can find the volume: \(V = s^3\)

(1) SA of one side of the cube is \(150/6 = 25\)
SA of one side of a cube is \(s^2\) so \(s^2 = 25\) and \(s = 5\) [Sufficient]

(2) Diagonal of a cube is \(\sqrt{3(s^2)}\) = \(5\sqrt{3}\)
\((5\sqrt{3})^2\) = \(25*3\) = \(75\) so \(3s^2 = 75\)
\(s^2 = 25\) and \(s = 5\) [Sufficient]

MAGOOSH OFFICIAL SOLUTION:

Another simple prompt, and again, we need the volume.

Statement #1 tells us surface area is 150. Well, for a cube, SA = 6s^2. If we know 150 = 6s^2, we can solve for s, which will allow us to calculate the volume. Statement #1 is by itself sufficient.

Statement #2 tell us the space diagonal has a length of \(5*\sqrt{3}\). Well, the three-dimensional version of the Pythagorean Theorem tell us that:

\((5*\sqrt{3})^2 = s^2 + s^2 + s^2\)

That would allow us to solve for s, which would allow us to calculate the volume. Statement #2 is by itself sufficient.

Both statements sufficient by themselves. Answer = D.
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It was an easy one.
Given: Q is a cube , so all sides are equal.
A) We know the surface area so length of a side can be calculated. SO A is sufficient. A or D can be the only answer . rule out B,C ,and E.
B) We know the diagonal length so again we can calculate the side length and gets volume of the cube. SO B is also sufficient.

A and B alone are sufficient. D is the answer

Given that Q is a cube we have find its volume

Statement 1 gives information about the total surface area of the cube = 150 sq.cm
we know that cube has 6 equal faces area of single face = 25 which in turn gives us the side as 5 cm
Volume of cube = 125 cu.cm
So sufficient

Statement 2 gives the length of longest diagonal of the cube as 5 *\(\sqrt{3}\)
this in turn gives us the side as 5 cm
Volume of cube = 125 cu.cm
So sufficient

Correct Answer - D

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