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Re: OG-12 DS # 122 [#permalink]
16 Jan 2012, 20:07
From the question, we do not know if the rectangular solid is a cube or a cuboid.
Fact 1 - Two adjacent faces of the solid have areas 15 and 24, respectively => This implies that the rectangular solid is a cuboid. We need to know the length of all 3 sides to calculate the volume. From the 2 adjacent face areas (15 & 24), we do not exactly know the length of the sides. If the sides are a, b & c => two adjacent faces could be made up of (a,b) and (b,c) OR (a,c) and (b,c).
Either way we cannot conclusively calculate all the 3 sides. (BCE)
Fact 2 - Each of the two opposite faces of the solid has area 40. Firstly this is infact a little confusing. I go as far as to think that all the faces have an area of 40. But I strongly believe in GMAC's ability to NOT confuse people and only give relevant information. So since the first fact dealt with adjacent faces, the 2nd fact deals with opposite faces. Opposite faces of a rectangular solid MUST have the same area but with this fact, we do not know which face we are talking about - just that one of the faces has an area of 40. And also that its opposite face is also 40 (which goes without saying!) And we still do not know the length of the sides that make up this face lest all the 3 sides. (1 X 40 = 40 OR 5 X 8 = 40). So this too is insufficient. (CE)
Combining both statements => we now know all the 3 face areas. 15, 24, and 40.
Say sides are a, b, c then
ab=15 bc=24 ac=40
Volume = abc Multiply all 3 values ab X bc X ac = (abc)^2 = (15 x 24 x 40) = whatever it is, we can calculate the value of abc, the volume.
So the answer is C.
I went back to the forums to confirm my method but yes most of them agree that the 2nd fact is confusing. And the explanation in the OG for the 2nd fact is that "...the volume is (5)(8)(x), which will vary as x varies.." - I think this is their way of saying that we only know the area of one face.