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
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On a certain date, Hannah invested $5,000 at x percent
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jjjinapinch
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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
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
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Jay@ManhattanReview
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We have: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
$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
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Jay@ManhattanReview
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Global Stats
We have: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
$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.
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Jay@ManhattanReview
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- Posts: 3008
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Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
We have: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
$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.
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Jeff@TargetTestPrep
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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.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
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.
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
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