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Difficulty:
35%
(medium)
Question Stats:
61% (01:05) correct
39%
(00:56)
wrong
based on 87
sessions
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What is the volume of a given cube?
(1) The ratio of an edge of the cube and the greatest distance between two points on the cube is \(1: \sqrt{3}\).
(2) The length of the diagonal across a face of the cube is 2.
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(1) The ratio of an edge of the cube and the greatest distance between two points on the cube is \(1: \sqrt{3}\).
(2) The length of the diagonal across a face of the cube is 2.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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gmatexam439
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Joined: 28 Mar 2017
Last visit: 18 Oct 2024
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Location: India
Concentration: Finance, Technology
GMAT 1: 730 Q49 V41
GPA: 4
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Bunuel
B
1. the diagonal of a cube is always = root 3* side
therefore any cube will have stmt 1 true.
insufficient
2. diagonal = root 2* side
therefore sufficient, since we can find the side, hence the volume
Schools: Alberta"19 Oxford "21 (A)
Posts: 8
Can someone please help explain the answer
How can do you find the sides from the diagonal
Posted from my mobile device
How can do you find the sides from the diagonal
Posted from my mobile device
Bunuel
IF YOU FIND MY SOLUTION HELPFUL, PLEASE GIVE ME KUDOS
(1). The ratio of an edge of a cube and the greatest distance between two points on the cube is 1:root3. This actually provides no information. When we have a cube, diagonal of a face is root2*side length, and the greatest distance between two points = sqrt (side length^2 +(side length *root2)^2) = sqrt( side length^2 + 2 side length squared)= sqrt(3*side length squared) = side length * root 3 per the pythagorean theorem. picking values for the side length will give us corresponding values for the diagonal of the cube. For example if side length = 1, we have a voume of 1^3 = 1 with face diagonal = 1*root2 and cube diagonal 1*root 3, but if our side length = 2 we have volume 2^3 = 8, with face diagonal 2*root 2 and cube diagonal 2*root3 NS
(2) The length of the diagonal across a face is 2. Per the pythagorean theorem, any square face with diagonal 2 will be found by solving 2 = 2x^2 --> x =1 (since the diagonal and 2 of the 4 sides make a right triangle. Since all sides of a cube are equal, both sides can be represented with x, thus x^2+x^2 =2^2 per Pythagorean theorem)
Thus, our volume = 1^3 = 1. Sufficient
The answer is B
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