Question

Of the 800 sweaters at a certain store, 150 are red. How many of the red sweaters at the store are made of pure wool? (1) 320 of the sweaters at the store are neither red nor made of pure wool. (2) 100 of the red sweaters at the store are not made of pure wool. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer 1

Answer:

Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

Step-by-step explanation:

Judging by the first sentence, there are 800 sweaters, 150 of which are red. Hence 800 - 150 = 650 sweaters are not red.

Statement (1) mentions that 320 of the sweaters at the store are neither red nor made of pure wool. This implies that of the remaining 650 non-red sweaters, 320 of them are not made of pure wool. It tells us then that there are 650 - 320 = 330 sweaters that are not red and that are not pure wool. So, it does not give information about red sweaters at all, whether pure wool or not.

Statement (2) says 100 of the red sweaters at the store are not made of pure wool. This means out of all 150 red sweaters, 100 of them are not made of pure wool. Then we have that 150 - 100 = 50 red sweaters are made of pure wool. This is the response to the question asked.

Hence, we see that statement (2) alone is enough, while statement (1) alone is not.