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

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
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Statement 1: If investment Y paid double the interest of investment X, then investment X must be double that of investment Y to get the same amount of interest earnt.

Therefore, the ratio of X:Y is 2:1, and so investment X is $8000, investment Y is $4000.

Statement 2 ain’t got enough info.

So answer is A.

Posted from my mobile device
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Simple interest = PRT/100, where P is principal, R rate of interest and T is time..
Here time is 1 year, as we are looking at simple annual interest..
SAI=PR/100..

1) statement I gives the two rate of interest as 3 and 6..
So z*3/100=(12000-z)*6/100..
It's a linear equation in z, you can find the value of z
Sufficient
2) statement II tells us that Robin invested $1000 more..
Nothing much
Insufficient

A
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Solution

Given:

• Robin invested total $12000 in two investments, X and Y
• The investments earned same amount of simple annual interest

To find:

• The amount (dollars) Robin invested in Y

Analysing Statement 1

• As per the information given in statement 1, investment X paid 3% simple interest whereas investment Y paid 6% simple interest
• If we assume that investment in X is P, then investment in Y will be (12000 – P)
• As the simple annual interest earned is same, we can write:

o \(\frac{P * 3}{100} = \frac{(12000 – P) * 6}{100}\)
• We can get the value of P as well as (12000 – P)

Hence, statement 1 is sufficient to answer

Analysing Statement 2

• As per the information given in statement 2, Robin invested more than $1000 in investment X

o From this, we cannot find out the exact investment in X and Y individually

Hence, statement 2 is not sufficient to answer

Hence, the correct answer is option A.

Answer: A
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For many folks(including me), who are wondering where is the time period specified, focus on the language of the question.
That is the trick in this otherwise simple question.

"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 ?"

"simple annual interest" and not "simple interest" so, the time period is 1 year.

Statement 2 gives no clarity on the boundaries of values of investment
Whereas statement 1 can give the exact value

Posted from my mobile device

Yes noticing the annual simple interest is the key, else statements are not sufficient

Posted from my mobile device

@Bunel, how is this correct when time is not defined in this question? How have we assumed that time is 1 year?

Will be waiting for your reply.

Gagan

Dear gagan0303
Take into consideration question stem:

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.

It signifies that we compare only "simple annual interest" to "simple annual interest"
In the dearth of the information we can only consider annual interest equal to 1 year.

Answer: Option A

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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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noticing the annual simple interest is the key