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Register now and save up to $200 Available with Beat the GMAT members only code ## On a certain date, Hannah invested$5,000 at x percent

This topic has 5 expert replies and 0 member replies
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

### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
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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 Answer: E 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. Answer: E _________________ Jeffrey Miller Head of GMAT Instruction ### GMAT/MBA Expert Jay@ManhattanReview GMAT Instructor Joined 22 Aug 2016 Posted: 1026 messages Followed by: 22 members Upvotes: 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
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
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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Jul 31, 2017 11:30 am
Hi jjjinapinch,

We're told that Hannah invested $5,000 at X percent simple annual interest and a DIFFERENT amount at Y percent simple annual interest. We're asked for the amount that Hannah invested at Y percent. This DS question can be solved by TESTing VALUES. 1) The total amount of interest earned by Hannah's two investments in one year was$900.

Based on the information in the prompt, we can create the following equation:

($5,000)(X/100) + ($Z)(Y/100) = 900

You can see that there are 3 variables, but just one equation - so there are likely lots of different possible values for Z. Here are two possibilities:

X = 6.... so ($5000)(6/100) =$300
Z = $10,000 and Y = 6... so ($10,000)(6/100) = $600 And the answer to the question is$10,000

X = 6.... so ($5000)(6/100) =$300
Z = $20,000 and Y = 3... so ($20,000)(3/100) = $600 And the answer to the question is$20,000
Fact 1 is INSUFFICIENT

(2) Hannah invested the $5,000 at 6 percent simple annual interest. The same two examples that I listed in Fact 1 also 'fit' Fact 2 (and create the same two different results): X = 6.... so ($5000)(6/100) = $300 Z =$10,000 and Y = 6... so ($10,000)(6/100) =$600
And the answer to the question is $10,000 X = 6.... so ($5000)(6/100) = $300 Z =$20,000 and Y = 3... so ($20,000)(3/100) =$600
And the answer to the question is $20,000 Fact 2 is INSUFFICIENT Combined, we have no additional work to do - the two examples we have already 'fit' both Facts and produce two different answers. Combined, INSUFFICIENT Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert Jay@ManhattanReview GMAT Instructor Joined 22 Aug 2016 Posted: 1026 messages Followed by: 22 members Upvotes: 470 Mon Jul 31, 2017 9:27 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
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

Locations: New York | Singapore | London | Dubai | and many more...

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
Posted:
1026 messages
Followed by:
22 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

Locations: New York | Singapore | London | Dubai | and many more...

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