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[email protected]: Master | Next Rank: 500 Posts; Posts: 429; Joined: Wed Sep 19, 2012 11:38 pmFollowed by: 4 members; Thanked: 6 times

by [email protected] » Thu May 09, 2013 2:23 am

122. What is the volume of a certain rectangular solid?
(1) Two adjacent faces of the solid have areas 15
and 24, respectively.
(2) Each of two opposite faces of the solid has
area 40.

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Source: Beat The GMAT — Problem Solving | Thu May 09, 2013 2:23 am

Atekihcan: Master | Next Rank: 500 Posts; Posts: 149; Joined: Wed May 01, 2013 10:37 pmFollowed by: 9 members; Thanked: 54 times

by Atekihcan » Thu May 09, 2013 2:41 am

Edit: Deleted the post as I was denying one of the basic principle of solving DS problem - You cannot use one statement to disprove the other one. The both statements are always true whether they are sufficient or not, individually or together.

Last edited by Atekihcan on Thu May 09, 2013 7:05 am, edited 1 time in total.

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Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Thu May 09, 2013 6:26 am

This is an actual OG question though, so it is important to note that this wording can come up... Having a clear view of what the GMAT tests goes a long way to not getting caught up in irrelevant details...

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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 » Thu May 09, 2013 6:32 am

[email protected] wrote:What is the volume of a certain rectangular solid?
(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
(2) Each of two opposite faces of the solid has area 40.

Target question: What is the volume of a certain rectangular solid (box)?

Statement 1: Two adjacent faces of the solid have areas 15 and 24, respectively.
There are several different rectangular solids that meet this condition. Here are two:
Case a: the dimensions are 1x15x24, in which case the volume is 360
Case b: the dimensions are 3x5x8, in which case the volume is 120
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Each of two opposite faces of the solid has area 40.
Definitely not sufficient

Statements 1 and 2 combined:
So, we know the area of each face (noted in blue on the diagram below).
Let's let x equal the length of one side.

Since the area of each face = (length)(width), we can express the other two dimensions in terms of x.

From here, we'll focus on the face that has area 40.
This face has dimensions (15/x) by (24/x)
Since the area is 40, we know that (15/x)(24/x) = 40
Expand: 360/(x^2) = 40
Simplify: 360 = 40x^2
Simplify: 9 = x^2
Solve: x = 3 or -3
Since the side lengths must be positive, we can be certain that x = 3

When we plug x=3 into the other two dimensions, we get 15/3 and 24/3
So, the 3 dimensions are 3, 5, and 8, which means the volume of the rectangular solid must be 120.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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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 » Thu May 09, 2013 6:35 am

Atekihcan wrote: First of all "rectangular solid" is a very vague term. It can be interpreted as some complex solid objects that are beyond the scope of GMAT.

"rectangular solid" is defined in the Official Guide (page 134 in the OG12 and OG13)
It's defined as what we know as a box

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Atekihcan: Master | Next Rank: 500 Posts; Posts: 149; Joined: Wed May 01, 2013 10:37 pmFollowed by: 9 members; Thanked: 54 times

by Atekihcan » Thu May 09, 2013 7:07 am

Brent@GMATPrepNow wrote:"rectangular solid" is defined in the Official Guide (page 134 in the OG12 and OG13)
It's defined as what we know as a box

Thanks Brent.
I take back what I said.
I don't know what I was thinking when I made that post.

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