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Volume of a rectangular solid

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Volume of a rectangular solid

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
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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
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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.
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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!

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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

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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!
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