A box measuring 54 inches long by 36 inches wide...

Expert replies

AAPL: Moderator; Posts: 2672; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Sun Jan 14, 2018 7:47 am

A box measuring 54 incches by long 36 inches wide by 12 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest numbre of cubes that can accomplish this objective?

A. 17
B. 18
C. 54
D. 108
E. 864

The OA is D.

I don't have clear this PS question, I should find the maximum common divisor of the 3 dimensions of the box, right? I appreciate if any expert explain it for me. Thank you so much.

Like this post

Source: Beat The GMAT — Problem Solving | Sun Jan 14, 2018 7:47 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Jan 14, 2018 10:38 am

Hi AAPL,

We're told that a box measuring 54 inches by 36 inches by 12 inches is to be filled entirely with identical CUBES and NO space is to be left unfilled. We're asked for the SMALLEST number of cubes that can accomplish this objective.

Since the length, width and height of a cube are the SAME - and we have to fill ALL of the space in the box - we need the length of the cube to be a factor of 54, 36 and 12 (and since we want the LEAST number of cubes possible, we need the greatest common factor of all three numbers). In this case, that would be 6.

6 divides evenly into 54 (9 times), 36 (6 times) and 12 (2 times), so the number of 6x6x6 cubes that will fill this box is (9)(6)(2) = 108 cubes

Final Answer: D

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

Contact Rich at [email protected]

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Aug 05, 2019 4:15 pm

AAPL wrote:A box measuring 54 incches by long 36 inches wide by 12 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest numbre of cubes that can accomplish this objective?

A. 17
B. 18
C. 54
D. 108
E. 864

Since we want to fit the smallest number of cubes in the box, we want each cube to be as large as possible. Since the greatest common factor of 54, 36 and 12 is 6, the largest cube is 6 x 6 x 6. Therefore, the smallest number of cubes we can fit in the box is:

(54 x 36 x 12)/(6 x 6 x 6) = 9 x 6 x 2 = 108

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review