GMAT Official Guide 2019 Robin invested a total of $12,000

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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.

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by GMATGuruNY » Sat Jun 30, 2018 1:42 am

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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.
Since X and Y constitute a total investment of $12,000, we get;
X + Y = 12,000

Statement 1:
Since 3% of X must yield the same amount of interest as 6% of Y, we get:
0.03X = 0.06Y
Since we have two variables (X and Y) and two distinct linear equations (X+Y=12000 and 0.03X=0.06Y), we can solve for the two variables.
Thus, the value of Y can be determined.
SUFFICIENT.

Statement 2:
It's possible that X = 2000 and Y = 10,000.
It's possible that X = 3000 and Y = 9,000.
Since Y can be different values, INSUFFICIENT.

The correct answer is A.
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by Brent@GMATPrepNow » Sat Jun 30, 2018 4:46 am

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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

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