Volume of a rectangular solid

Expert replies

buzzdeepak: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Mon Sep 17, 2012 12:27 pmFollowed by: 1 member; Thanked: 13 times; GMAT Score:710

by buzzdeepak » Tue Jan 22, 2013 10:49 am

What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas of 20 and 28.

(2) Each of two opposite faces of the solid has an area of 35.

The OA is C

I thought [spoiler] statement 1 (4x5 = 20, 4x7 = 28, So 4,5,7 would be the lengths of the rectangular solid)[/spoiler] would be sufficient... Please explain..

Thanks,
Deepak

Like this post

Source: Beat The GMAT — Data Sufficiency | Tue Jan 22, 2013 10:49 am

GMAT/MBA Expert

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 » Tue Jan 22, 2013 10:55 am

buzzdeepak wrote: I thought statement 1 (4x5 = 20, 4x7 = 28, So 4,5,7 would be the lengths of the rectangular solid) would be sufficient... Please explain..

Thanks,
Deepak

From statement 1, we can have several possible cases. Here are two:
case a: 2x10 = 20, 2x14 = 28, So the sides have lengths 2,10, and 14, which means the volume is 280
case b: 4x5 = 20, 4x7 = 28, So the sides have lengths 4,5, and 7, which means the volume is 140
So, statement 1 is not sufficient.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

buzzdeepak: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Mon Sep 17, 2012 12:27 pmFollowed by: 1 member; Thanked: 13 times; GMAT Score:710

by buzzdeepak » Tue Jan 22, 2013 11:00 am

Thanks Brent...

Lesson learned: If the problem is too easy (solvable within 20 secs), then need to slow down just a bit and re-evaluate the solution.

Like this post

GMAT/MBA Expert

Tommy Wallach: GMAT Instructor; Posts: 451; Joined: Thu Jan 21, 2010 11:58 amFollowed by: 120 members; Location: New York City; Thanked: 188 times; GMAT Score:770

by Tommy Wallach » Tue Jan 22, 2013 4:39 pm

Hey Buzz,

That's a really important general rule for DS. Unless you think you're bombing the test, and thus it's throwing really low level questions at you, if you can answer a question just by thinking about it in a few seconds (i.e. you haven't written anything down), the odds are really good you're thinking about it wrong! If you have to guess...don't pick that answer choice you got the easy way! It must be a different one!

-t

Tommy Wallach, Company Expert
ManhattanGMAT

If you found this posting mega-helpful, feel free to thank and/or follow me!

Like this post

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Tue Jan 22, 2013 7:46 pm

For those interested, below is an algebraic approach.

Assume the volume has sides of length a, b and c. We need the volume, so my rephrase is "What's the product abc?"

(1) Two adjacent faces of the solid have areas of 20 and 28

Since the faces are adjacent, they share a side (it doesn't matter which of a, b or c you share). We can write ab=20 and ac=28. From this info, we can find a^2 * b * c = 20 * 28. It's not possible to isolate abc without knowing the value of a (or of bc).

STATEMENT 1 IS NOT SUFFICIENT

(2) Each of two opposite faces of the solid has an area of 35.

Just use logic to evaluate this statement. we have a box with faces of area 35. Imagine standing the box on one of these faces (so the bottom and the top of the box would have area=35). It's not possible to pin down the exact volume because we have no idea how tall the box is. We need info about how long the other 4 faces are.

STATEMENT 2 IS NOT SUFFICIENT

MERGE STATEMENTS:
We have faces of 20, 28 and 35. We already decided that ab=20 and ac=28, so bc must equal 35. The product of all three faces would be a^2 * b^2 * c^2 = 20 * 28 * 35. The square root of this product is abc, the volume of the box.

Alternatively, since we know the size of all faces, we must have all the info to find out how big the box is (even if we didn't know how to calculate the volume).

THE STATEMENTS ARE SUFFICIENT TOGETHER.

Pick C

-Patrick

Check out my site: GMATFix.com

To prep my students I use this tool >> (screenshots, video)

Ask me about tutoring.

Like this post

GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Wed Jan 23, 2013 8:31 am

You and Tommy are right - if it feels too easy, it probably is!

The best way to slow down and reevaluate your assumptions on DS is to try to prove the statement insufficient, not to ask yourself whether it could be sufficient. That shift in perspective can make a huge difference.

With geometry DS, you should ask yourself "could I draw two different shapes with that same given information?" On this problem, when you read statement 1, a 4x5x7 box sprung to mind. Instead of assuming that that's the only case, you instinct should be to ask - "is there another box that would fit that statement?" As Brent said, it could be a 2x10x14, or a 1x20x28, etc.

When it comes to DS, be distrusting!

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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