Data Sufficiency

gmattoend wrote:A classroom of 80 students can practice swimming or playing tennis or both. They also have the option not to participate in any sport. How many students do practice only one sport?
1) 60% of those who do not play tennis also do not practice swimming.
2) 60% of those who play tennis also practice swimming.

To organize the data, use the following DOUBLE-MATRIX:


To answer the question stem, we need to determine the values in the two boxes with question marks (tennis but not swimming, swimming but not tennis).

Statement 1:
Let X = the total who do not participate in tennis.
The following matrix is yielded:

No information about the number who participate in tennis but not swimming.
INSUFFICIENT.

Statement 2:
Let Y = the total who participate in tennis.
The following matrix is yielded:

No information about the number who participate in swimming but not tennis.
INSUFFICIENT.

Statements combined:
The following matrix is yielded:

The bottom row indicates that Y+X = 80.
Since swimming but not tennis = 0.4X and tennis but not swimming = 0.4Y, we get:
Number in only one sport = 0.4X + 0.4Y = 0.4(X+Y) = 0.4(80) = 32.
SUFFICIENT.

The correct answer is C.