Data Sufficiency

BTGmoderatorDC wrote:A rectangular solid S, has dimensions 4 by 9 by k. What is the value of k?

(1) 4 < k < 9

(2) A cube of side 6 has the same volume as rectangular S.

OA B

Source: Princeton Review

Question: A rectangular solid S, has dimensions 4 by 9 by k.

Question: What is the value of k?

Let's take each statement one by one.

(1) 4 < k < 9

K can have any value. Insufficient.

(2) A cube of side 6 has the same volume as rectangular S.

Volume of cube = 6^3;
Volume of the rectangular solid S = 4*9*k

=> 6^3 = 4*9*k

k = 6. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorDC wrote:A rectangular solid S, has dimensions 4 by 9 by k. What is the value of k?

(1) 4 < k < 9

(2) A cube of side 6 has the same volume as rectangular solid S.

OA B

Target question: What is the value of k?

Given: A rectangular solid S, has dimensions 4 by 9 by k

Statement 1: 4 < k < 9
Since k can have ANY value between 4 and 9, statement 1 is NOT SUFFICIENT

Statement 2: A cube of side 6 has the same volume as rectangular solid S.
So (volume of cube) = (volume of rectangular solid)
Plug in values to get: (6)(6)(6) = (4)(9)(k)
Since we COULD solve this equation for k, we COULD answer the target question with certainty (of course we'd never waste time on test day solving the equation)
So, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent