gmat_winter wrote:At Western Springs School there are 150 total students who play either tennis, soccer, or both. Are there more students who play soccer than who play tennis?
(1) 50 students don't play soccer
(2) 80 students don't play tennis
OA [spoiler]B
[/spoiler]
Since 150 students play either soccer, tennis, or both -- and not one of these 150 students plays neither sport -- use the following matrix:
Statement 1: 50 students don't play soccer
Since total NS = 50, the following matrix is yielded:
Test EXTREMES.
Case 1: Both tennis and soccer = 0
In this case, total soccer = 100 and total tennis = 50.
Since more students play soccer than tennis, the answer to the question stem is YES.
Case 2: Both tennis and soccer = 100
In this case, total soccer = 100 and total tennis = 150.
Since more students play tennis than soccer, the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statement 2: 80 students don't play tennis
Since total NT = 80, the following matrix is yielded:
Again, test EXTREMES.
Case 3: Both tennis and soccer = 0
The following matrix is yielded:
In this case, total soccer = 80 and total tennis = 70.
Since more students play soccer than tennis, the answer to the question stem is YES.
Case 4: Both tennis and soccer = 70
The following matrix is yielded:
In this case, total soccer = 150 and total tennis = 70.
Since more students play soccer than tennis, the answer to the question is YES.
Since the answer is YES in both cases, SUFFICIENT.
The correct answer is
B.
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