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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Volume of a rectangular solid
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buzzdeepak
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Brent@GMATPrepNow
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From statement 1, we can have several possible cases. Here are two: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
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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buzzdeepak
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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.
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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Tommy Wallach
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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
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
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Patrick_GMATFix
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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
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
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ceilidh.erickson
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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!
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
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
