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20 Aug 2012, 03:25
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (01:29) correct
20%
(01:11)
wrong
based on 3093
sessions
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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.
(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.
20 Aug 2012, 03:25
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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.
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.
General Discussion
19 May 2016, 07:42
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Bunuel
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.
