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

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

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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

D

Source: Official Guide 2020

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AbeNeedsAnswers wrote:


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

D

Source: Official Guide 2020
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 following video: https://www.gmatprepnow.com/module/gmat-geometry/video/884

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

Here are a few more DS Geometry questions to practice with:
- http://www.beatthegmat.com/good-ds-question-t270971.html
- http://www.beatthegmat.com/what-is-the-sum-of-angles-x-and-y-t274620.html
- http://www.beatthegmat.com/what-is-the-perimeter-t277326.html
- http://www.beatthegmat.com/geometry-triangles-t271836.html
- http://www.beatthegmat.com/ds-2-t278892.html
- http://www.beatthegmat.com/coordinate-geometry-t277659.html

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Hi All,

We're told that the figure above represents a box that has the shape of a CUBE. We're asked for the is the volume of the cube. While this question might appear a bit 'scary', there's a great 'logic shortcut' built into it - since we're dealing with a CUBE, we know that all of the dimensions are EQUAL. By extension, if we know ANY length connecting two of the 8 vertices on the cube, then we can figure out ALL of the other lengths (using other Geometry formulas, although we won't actually have to do any of that math here) - and ultimately determine the volume.

1) PR = 10 cm

Length PR is a diagonal that forms on each face of the cube, so it would be the hypotenuse of a 45/45/90 right triangle. With that measurement, we could calculate the exact values of the sides and calculate the volume. There would be only one answer.

Fact 1 is SUFFICIENT

2) QT = 5√6 cm

When dealing with a 'rectangular solid', the formula for calculating the length from one 'corner' of the shape to the 'opposite opposite' corner is:
√(L^2 + W^2 + H^2)

Since we're dealing with a cube, we know that the length, width and height are the SAME. We can refer to all of those lengths as "X", which gives us:
√(X^2 + X^2 + X^2) = √(3X^2) = 5√6

With one variable and one equation, we CAN solve for the value of X - and there would be just one value, so we could calculate the volume of the cube.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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Question=> What is the volume of the box?
$$Volume=s^3,\ and\ s^2+s^2+s^2=d^2$$
Where s= side and d=diagonal
$$d=S\sqrt{3}$$
Statement 1: PR=10 cm where PR=diagonal
$$10=S\sqrt{3}$$
$$S=\frac{10}{\sqrt{3}}$$
$$Volume=s^3=\left(\frac{10}{\sqrt{3}}\right)^3$$
$$Statement\ 1\ is\ thus\ SUFFICIENT$$

Statement 2:
$$QT=5\sqrt{6}\ where\ QT=diagonal$$
$$5\sqrt{6}=s\sqrt{3}\ $$
$$\frac{\left(5\sqrt{6}\right)}{\sqrt{3}}=s$$
$$volume=s^3=\left(\frac{5\sqrt{6}}{9}\right)^3$$
$$Statement\ 2\ is\ also\ SUFFICIENT$$

Answer = option D

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