What is the volume of a certain rectangular solid?

Question

(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.

ynaikavde · Answer

if 20 and 28 are area of adjacent faces they share a side

20= 2*2*5
28=2*2*7

So we can have two possibilities rectangular solid (l,b,h)= (4,5,7) or (2,10,14)
volume is different for both, A insufficient.
Statement b states that opposite faces have area as 35 which confirms its (4,5,7), but as such alone its insufficient.
together they confirm its (4,5,7) hence C.

buddyisraelgmat · Answer

Ans - B

Stmnt 1 - Clearly insuff

Stmnt 2 - Each of two opposite faces of the solid has an area of 35.

lb = 35
bw = 35
lw = 35

(lbw)^2 = 35^3
Hence we can find lbw i.e. Volume

Whats OA?

chetan2u · Answer

hi,
 there can be various other options ..the sides need not be integer values.

chetan2u · Answer

Statement two is not sufficient alone...
there are three pair of opposite faces... (L,B),(H,B),(H,L)...
so only one is given so it is not sufficient..

chetan2u · Answer

ans C..

question asks us the volume so we need to find L*B*H and NOT values of L,B and H..

1) statement one tells us areas of two faces so we know LB and BH.. but there can be various combinations of integers/ fraction .... insufficient..
2) statement two gives us one of the faces.. not sufficient

combined we see we have areas of all three faces, and here we can find sides but if we think we can find L,B and H,  if these were variables that could take any value, there would be a set of negative values too...  
but we dont require to know individual sides to answer the question...
product of all three faces =(LB)*(BH)*(LH)=(LBH)^2=(20*28*35)=140^2... so volume =140...sufficient

EMPOWERgmatRichC · Answer

Hi All,

It looks like most of the posters have correctly determined that neither of the individual Facts is sufficient on its own, so I won't rehash any of that here.

When combining Facts, we end up with the 3 areas of the 3 faces....

LW, WH and LH are represented (in some order) by the numbers 20, 28 and 35

Since the prompt asks us for the VOLUME of the solid (V = LWH) we don't have to figure out the specific values of L, W and H, as long as we know what they are (in some order).

We could set up a "system" of equations using these values:
eg.
LH = 20
WH = 28
LW = 35

Here, we have 3 variables and 3 unique equations, so we CAN solve it (and there will be just one answer for this specific example). Playing around a bit with the numbers, you should be able to see that the individual measurements are 4, 5 and 7 (in some order), so the Volume = (4)(5)(7) = 140. There is NO other option. Combined, SUFFICIENT.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION

Answer: C

To find the volume, we’re going to need values for each of the 3 dimensions. Statement 2 is easier to start with. With an area of 35, the face could be 1 x 35 or 5 x 7. Even if we can narrow it down to exact dimensions, we’re still missing the third dimension. Insufficient. Statement 2 tells us that two adjacent faces have areas of 20 and 28. We also know that adjacent faces share one dimension; we can call them xy and xz, where x is the shared dimension. There are many possible situations: xy has dimensions of 4x5 and the is 4 x 7, or xy has dimensions of 1 x 20 and xz is 1 x 28, or xy = 2 x 10 and xz = 2 x 14. Insufficient. When combined, we know the third side must have dimensions of 5 x 7, which means that xy=4 x 5 and xz=4 x 7. Thus, volume is equal to 4 * 5 * 7, so the correct answer is C.

dabhishek87 · Answer

In statement 2, it says each of two opposite faces. Does this not mean that all of the opposite faces? L*B,B*H,H*B =35? If it says, one pair/two of the opposite faces then it can be taken as L*B=35 and other faces unknown?

bumpbot · Answer

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What is the volume of a certain rectangular solid?

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