Samantha investes i1 dollars in bond X, which pays r1

[BTGmoderatorLU]

Source: Manhattan Prep

Samantha invests i1 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

[Jay@ManhattanReview]

Source: Manhattan Prep

Samantha invests i1 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

Simple interest earned on the first investment = i1*r1*1/100 =i1*r1/100;
Simple interest earned on the second investment = i2*r2*1/100 =i2*r2/100;

We have to determine whether i1*r1/100 > i2*r2/100, or i1*r1 > i2*r2.

Let's take each statement one by one.

1) (r1)^2 > (r2)^2.

=> r1 > r2 since rates cannot be negative. Insufficient.

2) The ratio of i1 to i2 is larger than the ratio of r1 to r2.

i1/i2 > r1/r2.

Can't determine whether i1*r1 > i2*r2. Insufficient.

(1) and (2) together

From r1 > r2, we get r1 / r2 > 1. And from i1/i2 > r1/r2, we get that i1/i2 > 1 => i1 > i2.

Since i1 > i2 and r1 > r2, we have i1*r1 > i2*r2. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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