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Some amount of money is invested in an account at \(r\) percent compound interest rate, the amount of investment will

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by Vincen » Wed Nov 18, 2020 10:59 am

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Difficulty—

Some amount of money is invested in an account at \(r\) percent compound interest rate, the amount of investment will double in \(\dfrac{70}{r}\) years. If the amount gets \(4\) times in \(‘‘n"\) years, is \(n < 10?\)

(1) \(r < 14\%\)
(2) \(r > 12\%\)

Answer: A

Source: e-GMAT
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Source: — Data Sufficiency |
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Re: Some amount of money is invested in an account at \(r\) percent compound interest rate, the amount of investment wil

by deloitte247 » Thu Nov 19, 2020 10:59 am
$$2p=p\left(1+\frac{r}{100}\right)^{\frac{70}{r}}$$
$$\left(\left(2\right)^2=\left(1+\frac{r}{100}\right)^{\frac{70}{r}}\right)^2$$
$$if=\left(1+\frac{r}{100}\right)^{\frac{140}{r}}$$
so amount of investment doubles in 70/r years but 140/r years will make the amount 4 times, hence n = 140/r
$$1\ is\ \frac{140}{r}<10\ =\ r>14$$


$$Statement\ 1\ =>\ r<14\%$$
This provides a definite answer to the target question hence statement 1 is SUFFICIENT

$$Statement\ 2=>r>12\%$$
The value of r can either be 13 which is less than 1.4 or 15 which is greater than 14, so there is no definite answer to the target question hence statement 2 is NOT SUFFICIENT.


Since only statement 1 is SUFFICIENT,
Answer = A
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