The figure above represents a box that has the shape of a cube.

[BTGModeratorVI]

The figure above represents a box that has the shape of a cube. What is the volume of the box?

(1) PR = 10 cm
(2) QT = 5√6 cm

Answer: D
Source: Official Guide

[swerve]

The figure above represents a box that has the shape of a cube. What is the volume of the box?

(1) PR = 10 cm
(2) QT = 5√6 cm

Answer: D
Source: Official Guide

We just need to know one side value since volume \(= s^3\)

From statement 1:

We are told \(PR \Rightarrow s\sqrt{2} = 10\), we can calculate the value of \(s\) from here. Sufficient \(\Large{\color{green}\checkmark}\)

From statement 2:

Diagonal of a cube \(=s\sqrt{3}\)
\(s\sqrt{3} = 5\sqrt{6} \Rightarrow\) we can calculate the value of \(s\) from here. Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, D

[Brent@GMATPrepNow]

The figure above represents a box that has the shape of a cube. What is the volume of the box?

(1) PR = 10 cm
(2) QT = 5√6 cm

Answer: D
Source: Official Guide

Target question: What is the volume of the box?

IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement.
This concept is discussed in much greater detail in the video below.

This technique can save a lot of time.

Notice that there are infinitely-many cubes...

...and, for each cube, we have different measurements for PR and QT, AND each one of these unique cubes has its very own volume.
So, if a statement LOCKS in the precise measurements of the cube, then that statement must be sufficient.

Statement 1: PR = 10 cm
Among the infinitely-many cubes that exist in the universe, ONLY ONE cube is such that PR = 10 cm
Since statement 1 locks in the size of the cube, it is SUFFICIENT

Statement 2: QT = 5√6 cm
Among the infinitely-many cubes that exist in the universe, ONLY ONE cube is such that QT = 5√6 cmcm
Since statement 2 locks in the size of the cube, it is SUFFICIENT

Answer: D

Cheers,
Brent