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(1) The sums of money invested are $12,000 and$9,000, respectively.
(2) The durations for which the sums are invested are 3 years and 5 years, respectively.

The OA is C.

Why the two statements need to be together to be sufficient?

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Jay@ManhattanReview GMAT Instructor
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Wed Sep 20, 2017 10:24 pm
Vincen wrote:
A man invested two different sums of money, under the same rate of simple interest, but for different periods of time. The total interest he obtained from both the investments was $2,250. What was the rate of interest? (1) The sums of money invested are$12,000 and $9,000, respectively. (2) The durations for which the sums are invested are 3 years and 5 years, respectively. The OA is C. Why the two statements need to be together to be sufficient? Say the two sums are$X and $Y, the rate of interest is r% and periods for the sums are n and m years, respectively. Thus, we have, [Xrn/100] + [Yrm/100] = 2250 Xrn + Yrm = 225000 Statement 1: The sums of money invested are$12,000 and $9,000, respectively. We have X =$12,000 and Y = \$9,000. But we cannot get the value of r since the values of n and m are not known. Insufficient.

Statement 2: The durations for which the sums are invested are 3 years and 5 years, respectively.

We have n = 3 and m = 5. But we cannot get the value of r since the values of X and Y are not known. Insufficient.

Statement 1 & 2:

We have the values of X, Y, n, and m, so we can get the value of r. Sufficient.

There is no need to calculate the value of r as this is a DS question; you only need to be sure that the calculated value would be unique.

Hope this helps!

-Jay
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