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).
If you believe you have found an error in this question or explanation, please contact us and include the question title or URL in your message.