An exam was taken by a group of undergraduate students and graduate st

Official Explanation

We have three groups here, a big group and the two subgroups that make up the big group. We know the average of the big group, and we're trying to answer a question about the average of one of the subgroups, the undergraduates. Let's go to the statements, evaluating them separately first, as always.

Statement (1) tells us the average score of the graduate students. Analysis by cases is swift here. Case I: there are an equal number of grad students and undergrad students. In that case, the average for the undergrads would be 95, because only that way would the "pull" on both sides of the overall average be equally balanced. Case II: there are way more undergrads than grad students. If there are five times more undergrads, their average could be merely 91 and the overall average could be 90. Given that both cases are permitted by Statement (1), Statement (1) doesn't give enough information for us to answer the question definitively and it's insufficient.

Statement (2) is pretty clearly insufficient. Analysis by cases can dispel any doubts we might have. For all we know from Statement (2) alone, all of the scores in the group might be exactly 90. Or we could have some other sort of spread in which there are a small number of undergrads with quite high scores. Insufficient.

When we combine the statements, we can make sense of it by starting with a limiting case. As we discussed above in the context of Statement (1) alone, if the grad average is 85, and there are equally many grad students and undergrad students, the undergrad average would be exactly 95, so the pull down from the overall average balances the pull up. But that's not the case: there are more grads. That adjustment increases the pull down. To preserve the overall balance at 90, the undergrads, fewer in number, must average at a higher score than 95. Therefore the answer to the question posed must be, "Yes." We have been given sufficient information.

The correct answer is (C).

Video Explanation