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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