What amount did Jean earn from the commission on her sales

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OFFICIAL GMAT EXPLANATION

Let A be the amount of Jean’s sales in the first half of 1988. Determine the value of A.

(1) If the amount of Jean’s sales in the first half of 1988 was $10,000, then her commission in the first half of 1988 would have been (5%)($10,000) = $500. On the other hand, if the amount of Jean’s sales in the first half of 1988 was $100,000, then her commission in the first half of 1988 would have been (5%)($10,000) = $5,000; NOT sufficient.

(2) No information is given that relates the amount of Jean’s sales to the amount of Jean’s commission; NOT sufficient.

Given (1) and (2), from (1) the amount of Jean’s commission in the first half of 1988 is (5%)A. From (2) the amount of Jean’s sales in the second half of 1988 is A + $60,000. Both statements together do not give information to determine the value of A. Therefore, (1) and (2) together are NOT sufficient.

The correct answer is E; both statements together are still not sufficient.

Solution:

We need to determine the amount Jean earned from the commission on her sales in the first half of 1988.

Statement One Alone:

Since we don’t know the total amount of Jean’s sales in the first half of 1988, knowing only her commission rate is not sufficient to determine the amount of her commission in the first half of 1988.

Statement Two Alone:

Since we know neither the total amount of Jean’s sales in the first half of 1988 nor the commission rate, statement two is not sufficient to determine the amount of her commission in the first half of 1988.

Statements One and Two Together:

With the two statements, we still don’t know the total amount of Jean’s sales in the first half of 1988; thus, we can’t determine the amount of her commission in the first half of 1988.

Answer: E

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