On a certain date, Hannah invested $5,000 at x percent simple annual

SOLUTION

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.

Answer: E.
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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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Ha! When I first read the question, I thought "Why is Hannah investing money while out on a date with someone?"

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