DS 122 OG 12

[skprocks]

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.

Please provide an explannation.The second statement is not clear to me."Each" of Two Opposite faces,does this mean that all pairs of opposite faces have an area 40.Or,It means that a single pair of opp faces have an area 40.

OA: C

[uwhusky]

Oh...I get it =).

[Rahul@gurome]

In a rectangular solid, there are 6 faces let's say A, B, C, D, E and F from among which we can have 3 pairs such that two faces of each pair will have the same area and will be opposite. For example A and D will be opposite and have the same area.
B and E will be opposite and have the same area.
C and F will be opposite and have the same area.
What the second statement is saying that out of these 3 pair one pair will be of area 40.

Solution:
Obviously each statement alone is not sufficient to answer the question.
Let us check after combining both the statements.
Let the sides of the solid be a, b and c.
So ab =15, bc = 24 and ac = 40.

What we need is abc.
Now (abc)^2 = 15*24*40 = 14400
Or abc is 120.

The correct answer is hence (C).