gmatt1476 wrote:
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.
DS15650.02
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 = 4000Case b:
In this case,
the volume = 40 x 40 x 5 = 8000Since 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 = 4000Case b:
In this case,
the volume = 20 x 20 x 30 = 12000Since 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 = 4000Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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