This question is from Official Guide and Official Answer is C. About rectangular solid:
[img]gmatclub/forum/download/file.php?id=12547[/img]
In a rectangular solid,
all angles are right angles, and
opposite faces are equal, so rectangular solid can have maximum 3 different areas of its faces, on the diagram: yellow, green and red faces can have different areas. I say at max, as for example rectangular solid can be a cube and in this case it'll have all faces equal, also it's possible to have only 2 different areas of the faces, for example when the base is square and the height does not equals to the side of this square.
Volume of rectangular solid is Volume=Length*Height*Depth.
BACK TO THE ORIGINAL QUESTION:
What is the volume of a certain rectangular solid?(1) Two adjacent faces of the solid have areas 15 and 24, respectively --> let the two adjacent faces be blue and yellow faces on the diagram --> \(blue=d*h=15\) and \(yellow=l*h=24\) --> we have 2 equations with 3 unknowns, not sufficient to calculate the value of each or the product of the unknowns (\(V=l*h*d\)).
To elaborate more:
If \(blue=d*h=15*1=15\) and \(yellow=l*h=24*1=24\) then \(V=l*h*d=24*1*15=360\);
If \(blue=d*h=5*3=15\) and \(yellow=l*h=8*3=24\) then \(V=l*h*d=8*3*5=90\).
Two different answer, hence not sufficient.
(2) Each of two opposite faces of the solid has area 40 --> just gives the areas of two opposite faces, so clearly insufficient.
(1)+(2) From (1): \(blue=d*h=15\), \(yellow=l*h=24\) and from (2) each of two opposite faces of the solid has area 40, so it must be the red one: \(red=d*l=40\) --> here we have 3 distinct linear equations with 3 unknowns hence we can find the values of each and thus can calculate \(V=l*h*d\). Sufficient.
To show how it can be done: multiply these 3 equations --> \(l^2*h^2*d^2=(l*h*d)^2=15*24*40=24^2*5^2\) --> \(V=l*h*d=24*5=120\).
Answer: C.
Hope it helps.
Attachment:
800px-Cuboid.png
Can you explain why the volume is just not the lowest common multiple of ab and bc?
i.e. - ab = 15 = 5 x 3, bc = 24 = 8 x 3. There only one combination possible that = abc = 5 x 8 x3. You can do it for whichever way you want to arrange the faces in your calculations.