What is the Volume of Cubical Box in Cubic Centimeter? GMAT Data Sufficiency

Question: What is the volume of cubical box in cubic centimeter?

1. One face of the box has area of 36 sq cms.
2. The longest diagonal of the box is 18 cms.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“What is the volume of cubical box in cubic centimeter?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer: D
Solutions and Explanation
Approach Solution (1):

(1) Area = \(a^2\)= 36

Thus a = 6
Volume =\(a^3=6^3\)

Hence sufficient

(2). Please see attached fig. below

Given D = 18

\(d^2=a^2+a^2\)

Thus d in terms of a can be written
Again in triangle having hypotenuse as D
We have \(d^2=a^2+d^2\)

Or \(3a^2=18^2\)

Thus a can be calculated and hence the volume = \(d^3\)

Sufficient

Correct Option: D

Approach Solution (2):

1. Given the area of one face, you know the side of length which is sufficient to find the volume.

Sufficient

2. Given the diagonal of one face, you can determine the side length using the Pythagorean Theorem.

Sufficient

Correct Option: D

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