Explanation

We have a question about averages. When dealing with averages, our preferences are either, first, to focus on the total sum of the items averaged, and, second, to focus on the fact that the differences of all the elements from the average must sum to zero or "balance out." On to the statements, separately first.

Statement (1) gives a pretty healthy chunk of information. We can compare sums of the elements. If the average of the seven highest scores is 95, then those scores sum to . We desire to know whether the sum with the lower three is greater than . The question is whether the remaining three make of the difference of . Since the minimum score is 80, the bottom three must sum to at least , which is greater than 235. Therefore, the sum of all 10 must be greater than 900, meaning the average of all 10 must be greater than 90. We are able to answer the question definitively, so Statement (1) is sufficient.

Statement (2) gives us less information, because we know little about the top range of these numbers. The average of the lower four numbers is 85. One of these numbers is 80, so the other three could be 86, 87, and 87. In that case, the upper six numbers could all be, say, 88, and then the average of those six is 88, and the answer to the question is "no." On the other hand, consider a Case II: the lowest four scores could still be 80, 86, 87, and 87, but the average of the upper six could be 200. That case is allowed by this data statement, and in that case, the answer to the question is "yes." We lack sufficient information to answer the question definitively, so Statement (2) is insufficient.

The correct answer is (A).