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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Sat Mar 14, 2020 6:55 am

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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

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Source: Beat The GMAT — Data Sufficiency | Sat Mar 14, 2020 6:55 am

swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Sat Mar 14, 2020 2:45 pm

BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:55 am

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

by Brent@GMATPrepNow » Sun Mar 15, 2020 4:50 am

BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:55 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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