# GMAT OFFICIAL GUIDE DS – A total of \$60,000 was invested…

## Solution:

We are given that \$60,000 was invested for 1 year. We are also given that part of the investment earned x percent simple annual interest and the rest earned y percent simple annual interest. We are also given that the total interest earned was \$4,080. Let’s start by defining a variable.

b = the amount that earned x percent simple interest

Using variable b, we can also say:

60,000 – b = the amount that earned y percent simple annual interest

Since we know that the total interest earned was \$4,080, we can create the following equation:

b(x/100) + (60,000 – b)(y/100) = 4,080

Note that in the equation above, we express “x percent” as x/100 and “y percent” as y/100 in the same way that we would express, say, 24 percent as 24/100.

Statement One Alone:

x = 3y/4

Although we have an equation with x and y, we still need a third equation to be able to determine the value of x because our equation from the given information has three variables. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

From our given information we know that b is the amount that earned interest at the rate of x percent per year and that 60,000 – b is the amount that earned interest at the rate of y percent per year. Thus, we can create the following equation:

b/(60,000 – b) = 3/2

Without a third equation, statement two alone is not sufficient to determine the value of x. We can eliminate answer choice B.

Statements One and Two Together:

From the given information and statements one and two we have the following 3 equations:

1) b(x/100) + (60,000 – b)(y/100) = 4,080

2) x = 3y/4

3) b/(60,000 – b) = 3/2

Since we have 3 independent equations with variables x, y, and b, we are able to determine the value of x.