This question is from Official Guide and Official Answer is C.

About rectangular solid:
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 are 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.
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Let the sides be a,b,c

(1) ab=15 & bc=24. Not enough to calculate abc which is the volume. Insufficient

(2) Do you understand very well the second statement? Yes, its clear, it means that if you pick any of the two, it will have area=40.
Not enough to calculate volume, just one area provided

(1+2) Now we know all three areas, ab, bc, ca as 15,24,40
If you multiply all three, a^2b^2c^2 = 15x24x40. Just take the square root to get the volume (abc). Sufficient !!

Answer is (c)
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1) Two adjacent faces of the slid have areas 15 & 24, respectively.

2) Each of the opposite faces of the solid has area 40.

Let the length of the sides be a,b,c. Areas of each of the sides will be ab,bc,ca and the volume is abc

1. ab=15 ac=24 From these we cannot get individual values of a,b,c or the volume. So INSUFFICIENT

2. bc=40. From this we cannot get the volume. -- INSUFFICIENT

Combining we have:

ab=15
ac=24
bc=40

multiplying the LHS and RHS, you get:

(ab)(ac)(bc)=15*24*40
(a^2)(b^2)(c^2)=14400
or abc=120=Volume

So, C is the answer

How does 2nd statement imply that only bc=40,
the statement says that EACH of the opposite faces of the solid has area 40, so by this , even ac=ab=40, right?
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Guys,

I think that two statements contradict each other, because:
Statement 2 states that each face has area 40, but st. 1 says that some faces are 15 and 24 each...
(I assume that face=side)

Isn't it weird?

Bunuel, Can you clarify if 1 and 2 conflict in this case?
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There is no contradiction.
It is clearly mentioned each of the two opposite faces. That means the question is referring 2 opposite faces only.
READ CAREFULLY

If the area is 40 then 5*8 = 40 along with the 3*5 and 3*8 of the 1st statement is helpful in uniquely identifying the volume 3*5*8 as asked by the question.

Else area 15 and 24 could be because of the sides 1,15,24. The second statement removes this alternate solution.
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@ Bunuel - ha! amazing! : )

simply amazing bunuel.... i often get slipped in DS

If I refer to your drawing above. Blue face=15 Yellow face=24 and Red face=40. Bunuel, may be its just the wording that I don't understand:

"(1) Two adjacent faces of the solid have areas 15 and 24, respectively" means two faces have areas 15 and 24. We could say it ourselves that there will be two faces with these areas which are adjacent. How else?

>> I took this statement to mean this: Two adjacent faces could refer to: Red+Blue, Red+Yellow, Blue+Yellow. The assumption is that all faces are treated equal. Clearly, not all adjacent faces have area 15,24.

"(2) Each of two opposite faces of the solid has area 40" means that one pair of opposite faces has an area 40.

>> Each of two opposite faces = 40 to me means any opposite faces =40. I can understand if it said one pair, but I am not sure if "each of two" means "one pair". Clearly not all opposite faces have area = 40.

Thanks for your time and help.
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