QUESTION
Each student in a room is a sophomore, a junior, or a senior. Each of these students has exactly one of the categorizations of sophomore, junior, and senior. How many students in the room are seniors?
STATEMENT 1:
There are a total of 36 students in the room, of which 1/3 are sophomores.
STATEMENT 2:
There are 14 juniors in the room.
ANSWER SELECTION
(B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. (THIS IS CORRECT!)
(D) EITHER statement BY ITSELF is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
ANSWER EXPLANATION
Statement (1) tells us the total number of students in the room. This statement will also let us determine the number of sophomores, which is 1/3 of 36, or 12. Since no information is given about the juniors or seniors, we do not have sufficient information to answer the question. Statement (1) is insufficient. We can eliminate choices (A) and (D).
Statement (2) gives the number of juniors in the room. Since no information is given about the total number of students in the room or the number of sophomores in the room, this statement is insufficient. We can eliminate choice (B).
Taking the statements together, statement (1) gives us the total number of students in the room and the number of sophomores in the room, while statement (2) gives us the number of juniors in the room. We can subtract from the total number of people in the room the sum of the number of sophomores in the room and the number of juniors in the room to find the number of seniors in the room. The statements taken together are sufficient and choice (C) is correct.
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