Data Sufficiency

A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of X?

1. x= 3y/4

2. 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


Besides not getting the questions right, I read the explantion for the question out of the 12th edition and the manhattan OG Companion. Could someone explain how I could solve this faster than either explains?

Thanks!!!

I wouldn't worry about actually solving the problem - Just figure out what you need TO solve the problem, and based on the statements, whether those elements are provided by the statements.

I believe there are 2 pieces of information we need to solve for X.

1. What is Y? Y could be 100% interest or 0% interest, so we need to figure out Y in order to solve for x.
2. What portion of the 60k was the X interest applied to and what portion of the 60k was the Y interest applied to? (or P) - The portion charged x interest could be 1 dollar or all of the 60k.

To setup an equation I get:

60,000(x)(p) + 60,000(y)(1-p) = 4080

x and y are the decimal representations of the percentages.

Statement 1 tells us what Y is with relation to x, but we still don't know what piece of the 60k earned Y interest.

Statement 2 tells us that 60,000(p) / 60,000(1-p) = 2/3. I think we can reduce this to (p) / (1-p) = 2/3. Therefore, p = 2/5

Together.

60,000(x)(2/5) + 60,000(4x/3)(3/5) = 4080.

We should see that we have enough to solve for x.

you could solve for x, but the math is a waste of time and you'd be better spent rolling with C and saving the time elsewhere.