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A man invested two different sums of money. . .

This topic has 1 expert reply and 0 member replies

A man invested two different sums of money. . .

Post Wed Sep 20, 2017 7:53 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post 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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    Thanked by: Vincen

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