Last visit was: 18 Nov 2025, 18:33 It is currently 18 Nov 2025, 18:33
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
705-805 Level|   Geometry|      
User avatar
gmatbull
User avatar
Joined: 21 Dec 2009
Last visit: 04 Feb 2018
Posts: 334
Own Kudos:
2,673
 [56]
Given Kudos: 20
Concentration: Entrepreneurship, Finance
Posts: 334
Kudos: 2,673
 [56]
A closed aluminum rectangular box has inner dimensions x centimeters Updated on: 06 Oct 2017, 01:16
Originally posted by gmatbull on 21 Oct 2012, 11:07.
Last edited by Bunuel on 06 Oct 2017, 01:16, edited 3 times in total.
Renamed the topic.
8
Kudos
Add Kudos
48
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

58% (02:52) correct 42% (02:40) wrong based on 527 sessions

History

Date
Time
Result
Not Attempted Yet
A closed aluminum rectangular box has inner dimensions x centimeters by y centimeters by z centimeters. Each of the six sides of the box is 1 centimeter thick. Calculate the volume of the aluminium, in cubic centimeters?


A. \(xyz + 8\)

B. \(2(xy + xz + yz + 4)\)

C. \(2(xy + xz + yz) – xyz\)

D. \(2(xy + xz + yz + x + y + z + 4)\)

E. \(2(xy + xz + yz + 2x + 2y + 2z + 4)\)

Show Spoiler
Are we really concerned with the extra 1cm thickness in calculating the volume? The thickness does not add to spaces to
be filled; so, how come it is affecting the volume?
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,078
 [15]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,078
 [15]
A closed aluminum rectangular box has inner dimensions x centimeters 22 Oct 2012, 07:58
9
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
gmatbull
A closed aluminum rectangular box has inner dimensions x centimeters by y centimeters by z centimeters. Each of the six sides of the box is 1 centimeter thick. Calculate the volume of the aluminium, in cubic centimeters?

A. xyz + 8
B. 2(xy + xz + yz + 4)
C. 2(xy + xz + yz) – xyz
D. 2(xy + xz + yz + x + y + z + 4)
E. 2(xy + xz + yz + 2x + 2y + 2z + 4)

Are we really concerned with the extra 1cm thickness in calculating the volume? The thickness does not add to spaces to
be filled; so, how come it is affecting the volume?
Show more

Inner volume of the box is \(xyz\) cubic centimeters.

Now, since each of the six sides of the box is 1 centimeter thick, then outer dimensions are \(x+2\) by \(y+2\) by \(z+2\) centimeters. Therefore, the volume of the box with aluminium is \((x+2)(y+2)(z+2)\) cubic centimeters.

The volume of the aluminium is the difference of these two: \((x+2)(y+2)(z+2)-xyz=2(xy + xz + yz + 2x + 2y + 2z + 4)\).

Answer: E.

OR:

Plug numbers: say \(x=y=z=1\), then the inner volume is 1 cubic centimeters and the volume of the whole box is \((1+2)(1+2)(1+2)=27\) cubic centimeters. The volume of the aluminium is 27-1=26 cubic centimeters.

Now, plug \(x=y=z=1\) and see which options yields 26: only answer choice E fits.

Answer: E.

P.S. For plug-in method it might happen that for some particular numbers more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.
General Discussion
User avatar
Vips0000
User avatar
Current Student
Joined: 15 Sep 2012
Last visit: 02 Feb 2016
Posts: 521
Own Kudos:
1,291
Given Kudos: 23
Status:Done with formalities.. and back..
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE:Information Technology (Computer Software)
Products:
My Reviews
Schools: Olin - Wash U - Class of 2015
Posts: 521
Kudos: 1,291
A closed aluminum rectangular box has inner dimensions x centimeters 21 Oct 2012, 11:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatbull
A closed aluminum rectangular box has inner dimensions x centimeters by y centimeters by z centimeters.
Each of the six sides of the box is 1 centimeter thick. Calculate the volume of the plastic, in cubic centimeters?

A. xyz + 8
B. 2(xy + xz + yz + 4)
C. 2(xy + xz + yz) – xyz
D. 2(xy + xz + yz + x + y + z + 4)
E. 2(xy + xz + yz + 2x + 2y + 2z + 4)

Are we really concerned with the extra 1cm thickness in calculating the volume? The thickness does not add to spaces to
be filled; so, how come it is affecting the volume?
Show more

What does plastic do? questions looks incomplete.

The most logical meaning we can draw out of it is that you are going to cover the alumunium box with the plastic. In such case you need to add +1 cm because inner dimensions are given and cover would be calculated based on outer dimensions.
Second case, if you are going to fill in the plastic - in that case you dont need to care about +1 cm. and inner volume should suffice.
Hope it helps.
avatar
fukirua
avatar
Joined: 21 Oct 2012
Last visit: 13 Dec 2013
Posts: 19
Own Kudos:
82
Given Kudos: 15
GMAT Date: 01-19-2013
Posts: 19
Kudos: 82
A closed aluminum rectangular box has inner dimensions x centimeters 23 Oct 2012, 19:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

\((x+2)(y+2)(z+2)-xyz=2(xy + xz + yz + 2x + 2y + 2z + 4)\).
Show more

The question itself is very clear and not hard but it took me ages to multiple three brackets without a mistake. Is there a trick?
Thanks
User avatar
rajeevrks27
User avatar
Retired Moderator
Joined: 26 Aug 2011
Last visit: 24 Jan 2016
Posts: 507
Own Kudos:
997
Given Kudos: 264
Status:Enjoying the GMAT journey....
Location: India
Posts: 507
Kudos: 997
A closed aluminum rectangular box has inner dimensions x centimeters 23 Oct 2012, 21:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fukirua
Bunuel

\((x+2)(y+2)(z+2)-xyz=2(xy + xz + yz + 2x + 2y + 2z + 4)\).

The question itself is very clear and not hard but it took me ages to multiple three brackets without a mistake. Is there a trick?
Thanks
Show more
You have to put pen to paper as verbal calculation of the bracket will make issues complicated.
Try solving first two brackets first and then multiply with the third one.
Also, to avoid careless mistakes, always follow a pattern so that you don't miss anything.
for eg ( a + b) ( c + d) = a( c + d) + b ( c + d) always multiply with a pattern .
Hope this helps.
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,325
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,325
A closed aluminum rectangular box has inner dimensions x centimeters 24 Oct 2012, 02:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fukirua
Bunuel

\((x+2)(y+2)(z+2)-xyz=2(xy + xz + yz + 2x + 2y + 2z + 4)\).

The question itself is very clear and not hard but it took me ages to multiple three brackets without a mistake. Is there a trick?
Thanks
Show more

Start with multiplying the first two in the product of the three factors:

\((x+2)(y+2)(z+2)=(xy+2x+2y+4)(z+2)\)

No need to fully carry out the other multiplication. You can see that there will be one term of \(xyz\), which will cancel out in the final expression with \(-xyz\).
In addition, you will have terms containing products of two factors - like \(xy, \,\,xz\), and \(yz\). All will have a coefficient of 2 in front.
Then the terms with \(x, \,\,y,\) and \(z\), all have a coefficient of 4 in front.
Answers A, B, and C can be eliminated. Between D and E, obviously E wins.
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 305
Own Kudos:
626
 [2]
Given Kudos: 134
Posts: 305
Kudos: 626
 [2]
A closed aluminum rectangular box has inner dimensions x centimeters 11 Dec 2013, 13:48
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
A closed aluminum rectangular box has inner dimensions x centimeters by y centimeters by z centimeters. Each of the six sides of the box is 1 centimeter thick. Calculate the volume of the aluminium, in cubic centimeters?

A. xyz + 8
B. 2(xy + xz + yz + 4)
C. 2(xy + xz + yz) – xyz
D. 2(xy + xz + yz + x + y + z + 4)
E. 2(xy + xz + yz + 2x + 2y + 2z + 4)

We are trying to find the volume of the aluminum, NOT the empty space inside the box.

In the INNER dimensions are x*y*z then the dimensions of the box including the one inch thick sides are going to be two CM greater as shown in the attached diagram (in a way, this is similar to a "walkway surrounding a rectangular garden" problem, except in 3 dimensions) Therefore, the length of the box (not just the interior dimensions) is (L+2) The width is (W+2) and the height is (H+2) --> (L+2)*(W+2)*(H+2) is the volume of the box if we consider the volume of the sides included. If we are to figure out the volume of JUST the sides we subtract from (L+2)*(W+2)*(H+2) the volume of the empty space (L*W*H)

(L+2)*(W+2)*(H+2) - (LWH)
(LW+2L+2W+4)*(H+2) - (LWH)
LWH+2LH+2WH+4H+2LW+4L+4W+8 - (LWH)
2LH+2WH+4H+2LW+4L+4W+8
2(LH+WH+LW+2H+2L+2W+4)

Answer E.
avatar
therussian203
avatar
Joined: 04 Jul 2017
Last visit: 30 Apr 2018
Posts: 2
Given Kudos: 6
Posts: 2
Kudos: 0
A closed aluminum rectangular box has inner dimensions x centimeters 02 Sep 2017, 09:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
gmatbull
A closed aluminum rectangular box has inner dimensions x centimeters by y centimeters by z centimeters. Each of the six sides of the box is 1 centimeter thick. Calculate the volume of the aluminium, in cubic centimeters?

A. xyz + 8
B. 2(xy + xz + yz + 4)
C. 2(xy + xz + yz) – xyz
D. 2(xy + xz + yz + x + y + z + 4)
E. 2(xy + xz + yz + 2x + 2y + 2z + 4)

Are we really concerned with the extra 1cm thickness in calculating the volume? The thickness does not add to spaces to
be filled; so, how come it is affecting the volume?

Inner volume of the box is \(xyz\) cubic centimeters.

Now, since each of the six sides of the box is 1 centimeter thick, then outer dimensions are \(x+2\) by \(y+2\) by \(z+2\) centimeters. Therefore, the volume of the box with aluminium is \((x+2)(y+2)(z+2)\) cubic centimeters.

The volume of the aluminium is the difference of these two: \((x+2)(y+2)(z+2)-xyz=2(xy + xz + yz + 2x + 2y + 2z + 4)\).

Answer: E.

OR:

Plug numbers: say \(x=y=z=1\), then the inner volume is 1 cubic centimeters and the volume of the whole box is \((1+2)(1+2)(1+2)=27\) cubic centimeters. The volume of the aluminium is 27-1=26 cubic centimeters.

Now, plug \(x=y=z=1\) and see which options yields 26: only answer choice E fits.

Answer: E.

P.S. For plug-in method it might happen that for some particular numbers more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.
Show more

Hi - can you please help me understand how you know that based on the 1cm thickness, you should expand each side x/y/z by +2?

Thanks
avatar
PreiteeRanjan
avatar
Joined: 10 Feb 2017
Last visit: 04 Oct 2020
Posts: 42
Own Kudos:
28
Given Kudos: 25
Location: India
Schools: Rotman '20
GMAT 1: 710 Q49 V37
GPA: 4
Products:
My Reviews
Schools: Rotman '20
GMAT 1: 710 Q49 V37
Posts: 42
Kudos: 28
A closed aluminum rectangular box has inner dimensions x centimeters 04 Jun 2019, 23:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fukirua
Bunuel

\((x+2)(y+2)(z+2)-xyz=2(xy + xz + yz + 2x + 2y + 2z + 4)\).

The question itself is very clear and not hard but it took me ages to multiple three brackets without a mistake. Is there a trick?
Thanks
Show more
you certainly know that the xyz will be cancelled out and we will definitely have one 8 in the solution along with one set of double digit variable(such as xy,yz,zx,with what ever coeeficient may be ) and one set of single variable set suchas x,y,z.the suggested set is availble in only E.DONT TOUCH PEN AND PAPER ,BKZ BRAIN IS FASTER THAN HAND.:)
avatar
Bruvila
avatar
Joined: 06 Aug 2017
Last visit: 07 Apr 2022
Posts: 1
Given Kudos: 8
Posts: 1
Kudos: 0
A closed aluminum rectangular box has inner dimensions x centimeters 23 Sep 2021, 15:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I am astonished, today I took my test and this was my 2ND question! How is this possible? The solution look quite simple here, but I though arithmetically would take too much time. I solve it with smart numbers (2, 3 and 4), but took me ages to reach the solution:

Inner volume: 2x3x4=24
Exterior volume: 3x4x5-24 = 36.

Then you test all the possible solutions (took me like 4 minutes...)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
A closed aluminum rectangular box has inner dimensions x centimeters 20 Jul 2025, 10:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105355 posts
Krunaal
Tuck School Moderator
805 posts