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SVP
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What is the volume of a certain rectangular solid? (1) Two [#permalink]
 19 Jul 2004, 19:46
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17. 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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CIO
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C. Since we don't know if the sides are integers or not, 1 cannot be enough (though it would have been if we knew that for sure).
2 couldn't be enough no matter what.
together we know that the dimensions must be 8x5x3.
alternatively, we could say that
1)
lw=24
wh=15
Too many variables (again, not true if they're all integers)
2) lh=40; no connection to the rest of the figure
together) lw=24, wh=15, lh=40. Three variables and three equations --> sufficient.
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Director
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My ans is (B)...
(1) Insufficient.. Same reason as Ian..
(2) Question says... "Each of two opposite faces of the solid has area 40."
means lb = 40; bh = 40; lh = 40;
Multiply These three : (lbh) * (lbh) = 40^3
i.e. V^2 is known...
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SVP
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ian7777 wrote: C. Since we don't know if the sides are integers or not, 1 cannot be enough (though it would have been if we knew that for sure).
2 couldn't be enough no matter what.
together we know that the dimensions must be 8x5x3.
alternatively, we could say that
1)
lw=24
wh=15
Too many variables (again, not true if they're all integers)
2) lh=40; no connection to the rest of the figure
together) lw=24, wh=15, lh=40. Three variables and three equations --> sufficient.
ian777,
What does the following mean then "2) Each of two opposite faces of the solid has area 40".
--Bhai
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CIO
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Is this a real test question? That would help solve this word mystery. I read it as saying that there are two opposite sides that have an area of 40. JPV reads it as, "there are two pairs of opposite sides, each side with an area of 40".
The problem with that reading is that it would contradict number 1. It couldn't be true that from number 1 this figure has a pair of sides area 15, and a pair of sides area 24, and then from number 2 that it has two pairs of sides area 40 - we'd be talking about 8 sides all together.
In the GMAT, the two statements WILL NEVER contradict each other, because ultimately, they're talking about the same rectangular solid. So if this question comes from a real gmat book, or some other relyable source, I'd say it has to be C, and not B.
That, plus I still read the statement as saying that only 2 sides have an area of 40 each.
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Senior Manager
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I also got C,
what I don't get is how would A be sufficient if we knew that we're talking about integers here?
for example,
areas of adjacent sides are 24 and 15, we can have:
A. 8 by 3 by 5 = total volume of 120
B. 24 by 1 by 15 = total volume of 360
hence A can't be enough even if we knew the numbers were integers
Ian, what you do think?
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CIO
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you are right! 24x1x15 is also a solution. Broke my own rule there and forgot about 1!
good call!
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SVP
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ian777, the answer given is C and the source of this question is GMAT+
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close
