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jjjinapinch Senior | Next Rank: 100 Posts
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#### On a certain date, Hannah invested $5,000 at x percent Mon Jul 31, 2017 6:43 am 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.

Official Guide question

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### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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Mon Jul 31, 2017 9:28 pm
jjjinapinch wrote:
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. Official Guide question Answer: E We have:$5000 invested @ the rate of x%, and a different sum, say $P invested @ the rate of y%. We have to find out the value of P. Statement 1: The total amount of interest earned by Hannah's two investments in one year was$900.

=> [(5000*x*1)/100 + (P*y*1)/100] = 900

There are three variables, we cannot get the value of P. Insufficient.

Statement 2: Hannah invested the $5,000 at 6 percent simple annual interest. Clearly insufficient as this gives the value of x = 6%, but we cannot get the value of P. Insufficient. Statement 1 & 2 combined: From (1), we have [(5000*x*1)/100 + (P*y*1)/100] = 900 Plugging-in the value of x = 6 from (2) cannot get us the unique value of P. Insufficient. The correct answer: E Hope this helps! Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Singapore | London | Dubai | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert Jeff@TargetTestPrep GMAT Instructor Joined 09 Apr 2015 Posted: 530 messages Followed by: 6 members Upvotes: 39 Top Reply Wed Aug 09, 2017 11:25 am jjjinapinch wrote: 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.

Official Guide question
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 Hannahâ€™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.

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 + n(y/100) = 900

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

_________________
Jeffrey Miller Head of GMAT Instruction

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
Posted:
909 messages
Followed by:
18 members
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Mon Jul 31, 2017 9:28 pm
jjjinapinch wrote:
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. Official Guide question Answer: E We have:$5000 invested @ the rate of x%, and a different sum, say $P invested @ the rate of y%. We have to find out the value of P. Statement 1: The total amount of interest earned by Hannah's two investments in one year was$900.

=> [(5000*x*1)/100 + (P*y*1)/100] = 900

There are three variables, we cannot get the value of P. Insufficient.

Statement 2: Hannah invested the $5,000 at 6 percent simple annual interest. Clearly insufficient as this gives the value of x = 6%, but we cannot get the value of P. Insufficient. Statement 1 & 2 combined: From (1), we have [(5000*x*1)/100 + (P*y*1)/100] = 900 Plugging-in the value of x = 6 from (2) cannot get us the unique value of P. Insufficient. The correct answer: E Hope this helps! Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Singapore | London | Dubai | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert Jeff@TargetTestPrep GMAT Instructor Joined 09 Apr 2015 Posted: 530 messages Followed by: 6 members Upvotes: 39 Wed Aug 09, 2017 11:25 am jjjinapinch wrote: 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.

Official Guide question
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 Hannahâ€™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.

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 + n(y/100) = 900

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

_________________
Jeffrey Miller Head of GMAT Instruction

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
Posted:
909 messages
Followed by:
18 members
470
Mon Jul 31, 2017 9:28 pm
jjjinapinch wrote:
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. Official Guide question Answer: E We have:$5000 invested @ the rate of x%, and a different sum, say $P invested @ the rate of y%. We have to find out the value of P. Statement 1: The total amount of interest earned by Hannah's two investments in one year was$900.

=> [(5000*x*1)/100 + (P*y*1)/100] = 900

There are three variables, we cannot get the value of P. Insufficient.

Statement 2: Hannah invested the \$5,000 at 6 percent simple annual interest.

Clearly insufficient as this gives the value of x = 6%, but we cannot get the value of P. Insufficient.

Statement 1 & 2 combined:

From (1), we have

[(5000*x*1)/100 + (P*y*1)/100] = 900

Plugging-in the value of x = 6 from (2) cannot get us the unique value of P. Insufficient.

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

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