DS Question from Official Test

Cybermusings wrote: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 an area of 40

I'm not sure what (2) is referring to -- does it refer to 1 out of 3 pairs or
does it refer to all pairs (hence making it a cube).

Assuming that (2) is referring to 1 out of 3 pairs, my vote would be C

1 - insufficient. lb = 15 and bh or lh = 24.
2 - insufficient. We already know 2 sides should be equal

Using 1 & 2, we can solve for lbh and hence get volume.


If (2) is referring to "each" of the 3 pairs of opposite sides, then
the solid becomes a cube and we can hence find the volume. So, 2
will be sufficient.

Would appreciate if someone can clarify on what (2) means.

Alright well this is the way I interpreted it to be.



Since it said two adjacent faces have the areas of 15 and 24, I got one of the sides to be 15 as 5 x 3, (3 is the height, 5 is the width of the cube).

From the 3 of the height, I got the length to be 8, which is how its equal to 24, and since it said the sides are adjacent, well these are adjacent (at least to me they seem to be), so I assumed that.

Then, the biggest area, I got to be 8 x 5 which is 40, and it corresponds with statement 2.

I know it says that in the data sufficiency questions you shouldnt try to solve it, but truth be told, I can't NOT solve it, I find that it actually helps me, but I don't spend a lot of time solving it either.

Anyway, so I don't get how to answer these things because in this case to me the answer can be either A or C.

Choice B I find is not sufficient on its own, so therefore I would rule out D as well, but as for C, I'm a little iffy on that.

From Statement 1, we could have figured out that 8 x 5 would be 40 anyway, but I dunno, I think the fact that statement 2 said the area would be 40 just backed it up, so I'm unsure....but I think the statement would be A, that #1 is sufficient enough.

Anyone else?

arielsky wrote: From Statement 1, we could have figured out that 8 x 5 would be 40 anyway, but I dunno, I think the fact that statement 2 said the area would be 40 just backed it up, so I'm unsure....but I think the statement would be A, that #1 is sufficient enough.

Anyone else?

We cannot assume that the sides are actually "integers". So, A is not
sufficient.

would it be C then?

Answer is C.

1. insufficient. It gives the area of two faces.

2. insufficient. It gives the area of third face, which is 20.

Let l,b,h be length,breadth and height of the solid.

If we multiply the area of 3 faces

l^2 * b^2 * h^2 = 15*24*20

1.e l*b*h = volume = sqrt 15*24*20