Sorry, a typo : "by wording used in statement 2"

rajendraputta wrote:Hello all,
This question in OG 12 is pretty ambigous.

122. 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.

which two opposite faces does the 2nd statement refer to? By the wording used in statement I thought that l*b=40, b*h= 40, and h*l=40. So, i thought side must be square root of 40. But, OG answer takes the other face(other than 15 and 24) and its oppsite face to be of area 40 and says C is the right answer. Isnt it wrong to assume the other face to be of area 40???

Hi - data sufficiency is all about ambiguity! It's exactly when things are ambiguous that we don't have enough information to answer the question.

The problem is with your interpretation of (2). "Two opposite faces" of a rectangular solid are identical, so from (2) alone all that we know is that two of the 3 dimensions multiply to 40.

When we put the statements together, however, we have 3 different areas for 3 different sides. Since rectangular solids only have 3 different sides, we've created a unique solid and, accordingly, it must be possible to calculate the volume.

Since it's data sufficiency we don't actually have to, but if it were problem solving we'd set up 3 equations for our 3 unknowns:

l*w = 40
l*h = 24
h*w = 15

and solve, ignoring negative solutions (something we can always do in geometry problems).

Note that it's irrelevant which dimensions we put in each equation, we'll always get the same volume.

(Since vol = l*w*h = w*h*l = l*h*w = ...)