If all of the six faces of a concrete block are rectangular, what is the volume of the block?

[BTGModeratorVI]

If all of the six faces of a concrete block are rectangular, what is the volume of the block?

(1) Each of the four lateral faces of the block has an area of 200 square inches.
(2) The top of the block is square and has an area of 400 square inches.

Answer: C
Source: official guide

[Brent@GMATPrepNow]

If all of the six faces of a concrete block are rectangular, what is the volume of the block?

(1) Each of the four lateral faces of the block has an area of 200 square inches.
(2) The top of the block is square and has an area of 400 square inches.

Answer: C
Source: official guide

Target question: What is the volume of the block?

Statement 1: Each of the four lateral faces of the block has an area of 200 square inches.
There are many rectangular solids that satisfy statement 1. Here are two:

Case a:

In this case, the volume = 20 x 20 x 10 = 4000


Case b:

In this case, the volume = 40 x 40 x 5 = 8000

Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: The top of the block is square and has an area of 400 square inches.
There are many rectangular solids that satisfy statement 2. Here are two:


In this case, the volume = 20 x 20 x 10 = 4000


Case b:

In this case, the volume = 20 x 20 x 30 = 12000

Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that the top face is SQUARE and has an area of 400 square inches.
This means the length and width are both 20 inches long.
The only thing we don't yet know is the height of the block

Statement 1 tells us that the lateral faces each have an area of 200
Since the length and width are both 20 inches, this means the height must be 10 (since 20 x 10 = 200)

Now that we know the measurements of the length, width and height, we can be certain that the volume = 20 x 20 x 10 = 4000

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent