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On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest. What amount did Hannah invest at y percent simple annual interest?

(1) The total amount of interest earned by Hannah's two investments in one year was $900. (2) Hannah invested the $5,000 at 6 percent simple annual interest.

Practice Questions Question: 25 Page: 277 Difficulty: 650

On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest. What amount did Hannah invest at y percent simple annual interest?

Say the amount Hannah invested at y percent is I.

(1) The total amount of interest earned by Hannah's two investments in one year was $900. Given: \(5,000*\frac{x}{100}+I*\frac{y}{100}=900\). We have one equation and three unknowns, hence we cannot solve for I. Not sufficient.

(2) Hannah invested the $5,000 at 6 percent simple annual interest. Given: \(x=6%\). Not sufficient.

(1)+(2) We have that \(5,000*\frac{6}{100}+I*\frac{y}{100}=900\). We still have one equation and two unknowns, hence we cannot solve for I. Not sufficient.

"(2) Hannah invested the $5,000 at 6 percent simple annual interest."

We have the information about x + y = 6%, but we don't know what is exactly y or x, so unsufficient.

Although I agree that the answer is E, I'm not sure how you came up with X + Y = 5000. Hannah had two principles, one valued at 5,000 undergoing x interest and some unknown principle undergoing y interest.

On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest. What amount did Hannah invest at y percent simple annual interest?

Say the amount Hannah invested at y percent is I.

(1) The total amount of interest earned by Hannah's two investments in one year was $900. Given: \(5,000*\frac{x}{100}+I*\frac{y}{100}=900\). We have one equation and three unknowns, hence we cannot solve for I. Not sufficient.

(2) Hannah invested the $5,000 at 6 percent simple annual interest. Given: \(x=6%\). Not sufficient.

(1)+(2) We have that \(5,000*\frac{6}{100}+I*\frac{y}{100}=900\). We still have one equation and two unknowns, hence we cannot solve for I. Not sufficient.

Re: On a certain date, Hannah invested $5,000 at x percent [#permalink]

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19 Dec 2015, 15:50

Can someone tell me why can't I treat x and y as known? I was thinking that the answer should be (A), since from (A), we can represent the amount of money Hannah invested in y percent simple annual interest rate as "[900 - 5000*(x/100)]/[y/100]."

I don't think the question makes it clear that we should treat x and y as unknowns.

On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest. What amount did Hannah invest at y percent simple annual interest?

(1) The total amount of interest earned by Hannah's two investments in one year was $900. (2) Hannah invested the $5,000 at 6 percent simple annual interest.

Solution:

We are given that Hannah invested $5,000 at x percent simple annual interest and invested another amount at y percent simple annual interest. We need to determine the amount that she invested at y percent simple annual interest. We can let this amount be n.

Statement One Alone:

The total amount of interest earned by Hannah’s two investments in one year was $900.

Using statement one, we can set up the following equation: 5,000(x/100) + n(y/100) = 900

Multiplying the entire equation by 100 we have:

5,000x + ny = 90,000

Since we do not know the value of x or y, we cannot determine the value of n, and thus statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Hannah invested the $5,000 at 6 percent simple annual interest.

From statement two we know that x is 6 and thus we can determine how much interest Hannah made from her investment at x percent interest.

5,000 x 6/100 = $300

However, we still do not know how much money was invested at y percent simple annual interest. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From both statements we have the following equation:

300 + ny = 900

Since we do not know the value of y, we still cannot determine a value for n.

The answer is E.
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