Robin invested a total of $12,000 in two investments, X and Y, so that

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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.

Answer: A
Source: Official guide

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Let money invested in investment x = x
Let money invested in investment y = y


Target question => How many dollars did Robin invest in investment y?
i.e Find the value of y
Total investment => $12000 and x + y = $72000


Statement 1 => investment x paid 3% simple annual interests and investment y paid 6% simple annual interest
Annual interest paid by investment x = 3% of x = 0.03x
Annual interest paid by investment y = 6% of y = 0.06y
Since annual interest on the two investments are equal 0.03x = 0.06y


From question stem x + y = 12000 and x = 12000 - y
0.03(12000 - y) = 0.06y
360 - 0.03y = 0.06y
360 = 0.06y + 0.03y
360/0.09 = 0.09y/0.09
y = $4000
Statement 1 is SUFFICIENT


Statement 2 => Robin invested more than $1000 in investment x
We only know that x > $1000. The exact amount invested is unknown and the interest rate is unknown. Hence, the target question cannot be answered, statement 2 is NOT SUFFICIENT


Since only statement 1 is SUFFICIENT,
Answer = A

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BTGModeratorVI wrote:
Fri Aug 14, 2020 1:08 pm
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.

Answer: A
Source: Official guide
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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BTGModeratorVI wrote:
Fri Aug 14, 2020 1:08 pm
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.

Answer: A
Source: Official guide
Solution:

Question Stem Analysis:

We need to determine the amount invested in investment Y given that a total of $12,000 was invested in investments X and Y and the two investments earned the same amount of simple annual interest.

Statement One Alone:

Since we know investment Y paid 6 percent simple annual interest, which is twice 3 percent simple annual interest that investment X paid, then, in order for the two investments to earn the same amount of simple annual interest, the amount invested in investment Y needs to be half that in investment X. In other words, investment Y should be $4,000 (and investment X should be $8,000). Statement one alone is sufficient.

Statement Two Alone:

Knowing investment X is more than $1,000 does not allow us to determine the amount invested in investment Y. Statement two alone is not sufficient.

Answer: A

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