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A man invested two different sums of money. . .

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A man invested two different sums of money. . .

by Vincen » Wed Sep 20, 2017 7:53 am
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?
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » 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.

The correct answer: C

Hope this helps!

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-Jay
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