Data Sufficiency

BTGmoderatorLU wrote:Source: Princeton Review

At Western Spring School there are 150 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.

The OA is B.

Say,
the number of students who play ONLY Soccer = S;
the number of students who play ONLY Tennis = T; and
the number of students who play BOTH = B

Thus, S + B + T = 150

We have to find out whether S + B > T + B => S > T

Let's take each statement one by one.

(1) 50 students don't play soccer.

=> T = 50
=> S + B = 150 - 50 = 100

Case 1: If S > 50 and B ≤ 50, the answer is Yes.
Case 2: If S ≤ 50 and B > 50, the answer is No. No unique answer. Insufficient.

(2) 80 students don't play tennis.

=> S = 80
=> T + B = 150 - 80 = 70

Even if B = 0, or T is maximum = 70, we see that S (= 80) > T(= 70). The answer is Yes. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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