A rectangular solid S, has dimensions 4 by 9 by k. What is

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Oct 14, 2018 5:19 pm

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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

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Source: Beat The GMAT — Data Sufficiency | Sun Oct 14, 2018 5:19 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sun Oct 14, 2018 9:06 pm

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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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

by Brent@GMATPrepNow » Mon Oct 15, 2018 5:48 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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