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## Percent and Interest Problems

##### This topic has expert replies
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### Percent and Interest Problems

by swerve » Tue Feb 11, 2020 12:21 pm
Samantha invests i1 dollars in bond X, which pays r1 percent simple interest annually, and she invests i2 dollars in bond Y, which pays r2 percent simple interest annually. After one year, will she have earned more interest, in dollars, from bond X than from bond Y?

1) $$(r1)^2 > (r2)^2$$
2) The ratio of i1 to i2 is larger than the ratio of r1 to r2.

The OA is C

Source: Manhattan Prep

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### Re: Percent and Interest Problems

by Ian Stewart » Tue Feb 11, 2020 1:39 pm
swerve wrote:
Tue Feb 11, 2020 12:21 pm
Samantha invests i1 dollars in bond X, which pays r1 percent simple interest annually, and she invests i2 dollars in bond Y, which pays r2 percent simple interest annually. After one year, will she have earned more interest, in dollars, from bond X than from bond Y?

1) $$(r1)^2 > (r2)^2$$
2) The ratio of i1 to i2 is larger than the ratio of r1 to r2.

The OA is C

Source: Manhattan Prep
Since everything is positive, we can square root both sides in Statement 1. So Statement 1 just tells us the interest rate is higher on the first investment. That's not sufficient.

Statement 2 is not sufficient, since it will be true almost by default if the interest rate on the first investment is nearly zero and the interest rate on the second investment is, say, 10%. Then the first investment could earn more interest if a monstrous amount was invested in it compared to the second, or less if similar amounts were invested in both.

Using both Statements, we know the ratio of the first interest rate to the second is greater than 1, from Statement 1. Statement 2 tells us that the ratio of the amounts invested is even greater than that, so is certainly greater than 1, and more was invested in the first investment than in the second. If a larger amount was invested in the first investment, and at a higher interest rate, of course it made more money. So the answer is C.
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