Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

75% (01:06) correct 25% (00:52) wrong based on 1257 sessions

HideShow timer Statistics

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]

Show Tags

19 Dec 2015, 14:50

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.
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions