BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

MGMAT

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Tue May 04, 2010 12:36 am
Thanked: 4 times
by yuliawati » Mon Nov 01, 2010 11:00 pm
Guys, please help! how to solve this problem?

A certain cube is composed of 1000 smaller cubes, arranged 10 by 10 by 10. The top layer of cubes is removed from a face, then from the adjacent face above it, then from the adjacent face to the right of the first. The process is repeated on the same three faces in reverse order. Finally, a last layer is taken from the first face. How many smaller cubes have been removed from the larger cube?

(A) 488
(B) 552
(C) 612
(D) 722
(E) 900

OA later
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 905
Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members
Thanked: 378 times
GMAT Score:760

by Geva@EconomistGMAT » Tue Nov 02, 2010 12:28 am
I would probably just find what cube I have remaining, and subtract the new number of cubes from the 1000.
you start with 10*10*10.

Remove a top layer from the front, so the cube is only 9 cubes "wide": 10*9*10
shave a layer from the top face ("above it"), so the cube is only 9 cubes "high": 10*9*9
Now shave a layer from the side ("to the right of the first") so the cube is only 9 cubes "long": 9*9*9

Every time you shave a layer, you reduce 1 from one dimension, leaving the others as they are. Thus, if we repeat the process for all three dimensions (even in reverse order), we get 8*8*8. If we take another layer from the first face, we take another 1 from the width to get 8*7*8
How we call the dimensions "length, width height" does not really matter: the dynamic is the same, and the result will be two 8s and a 7.

Now the question asked how many have been removed, so the final answer is {original number - new number} = 10*10*10 - 8*8*7 = 1000 - 64*7 = 1000 - 448 = 552. Answer should be B.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Tue May 04, 2010 12:36 am
Thanked: 4 times

by yuliawati » Tue Nov 02, 2010 1:30 am
Great!! thank Geva!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 235
Joined: Wed Oct 26, 2016 9:21 pmFollowed by: 5 members
Thanked: 3 times

by Anaira Mitch » Sat Jan 14, 2017 4:17 pm
We can answer this by keeping track of how many cubes are lopped off of each side as the cube is trimmed (10 x 10 + 10 x 9 + 9 x 9 + ...), but this approach is tedious and error prone. A more efficient method is to determine the final dimensions of the trimmed cube, then find the difference between the dimensions of the trimmed and original cubes.

Let's call the first face A, second face B, and third face C. By the end of the operation, we will have removed 2 layers each from faces B and C, and 3 layers from face A. So B now is 8 cubes long, C is 8 cubes long, and A is 7 cubes long. The resulting solid has dimensions 8 x 8 x 7 cubes or 448 cubes. We began with 1000 cubes, so 1000 - 448 = 552. Thus, 552 cubes have been removed.

The correct answer is B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Wed Jan 18, 2017 7:19 pm
Here's a quick way:

We're removing three layers from the length, two layers from the width, and two layers from the height.

We originally had 10 * 10 * 10, but now we've got (10 - 3) * (10 - 2) * (10 - 2), or 448.

The difference between 1000 and 448 is the number that we've removed, so 1000 - 448, or 552.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1