The question is a "twist" on the typical Overlapping Sets question that you'll see on Test Day. Depending on the "restrictions" given in the prompt and the specific question that's asked, there are usually a few different ways to approach the work.
This particular prompt is designed in such a way that it can be solved with minimal note-taking and a bit of logic.
We're given a few facts to start off with:
1) There are 150 total students
2) They ALL play tennis, soccer OR both.
The question asks if more students play soccer than play tennis. This is a YES/NO question. The "key" to dealing with it is to remember that EVERY student plays at least one sport....
Fact 1: 50 students don't play soccer.
This tells us that these 50 students MUST play JUST tennis. But what about the other 100 students? We can deduce that they MUST play soccer, but they MIGHT also play tennis.....
All 150 students play tennis, then the answer to the question is NO.
99 play tennis, then the answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: 80 students don't play tennis.
This tells us that these 80 students MUST play JUST soccer. The other 70 students MUST play tennis, but it can't be any more than those 70. They might also play soccer, but whether they play soccer or not does NOT impact the question. We're asked if MORE students play soccer than play tennis. With this info, we know that the answer to the question MUST be YES.
Fact 2 is SUFFICIENT.
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