BTGmoderatorDC wrote:Robin invested a total of $12,000 in two investments, X and Y, so that the investments earned the same amount of simple annual interest. How many dollars did Robin invest in investment Y ?
(1) Investment X paid 3 percent simple annual interest, and investment Y paid 6 percent simple annual interest.
(2) Robin invested more than $1,000 in investment X.
Let X = The number of dollars invested in investment X
Let Y = The number of dollars invested in investment Y
Target question: What is the value of Y?
Given: Robin invested a total of $12,000 in two investments, X and Y, so that the investments earned the same amount of simple annual interest.
If the total investment is $12,000, we can write:
X + Y = 12,000
Statement 1: Investment X paid 3 percent simple annual interest, and investment Y paid 6 percent simple annual interest.
So, the annual interest paid by investment X = 0.03X and the interest paid by investment Y = 0.06Y
Since the annual interest on the two investments are EQUAL, we can write:
0.03X = 0.06Y
We now have the following system of linear equations:
X + Y = 12,000
0.03X = 0.06Y
Since we COULD solve this system for Y, we COULD answer the
target question with certainty (but we would never waste valuable time actually solving the system!)
Since we could answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: Robin invested more than $1,000 in investment X.
Since we don't know the exact value of the amount Robin invested in X, and since we don't know anything about the interest rates for the investments, we cannot answer the
target question with certainty.
So, statement 2 is NOT SUFFICIENT
ASIDE: If you're not convinced that statement 2 is not sufficient, consider these two cases:
Case a: X = 6,000, Y = 6,000, and the interest rate for each investment is 10%. Notice that the interest for each investment will be equal. Here, the answer to the target question is
Y = 6,000
Case b: X = 2000, Y = 10,000, the interest rate for investment X is 50%, and the interest rate for investment Y is 10%. Notice that the interest for each investment will be equal. Here, the answer to the target question is
Y = 10,000
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
