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20 Aug 2012, 03:25
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25% (medium)

Question Stats:

74% (01:06) correct 26% (00:52) wrong based on 1476 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. Practice Questions Question: 25 Page: 277 Difficulty: 650 _________________ Math Expert Joined: 02 Sep 2009 Posts: 46297 Re: On a certain date, Hannah invested$5,000 at x percent [#permalink]

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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. _________________ Intern Joined: 19 Apr 2012 Posts: 25 Re: On a certain date, Hannah invested$5,000 at x percent [#permalink]

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20 Aug 2012, 10:17

The Formula to calculate the interest is the following:

$$\frac{x}{100}*X + \frac{y}{100}*Y = Interest$$

$$X + Y = 5000$$
"The total amount of interest earned by Hannah's two investments in one year was $900." $$\frac{x}{100}*(5000-Y) + \frac{y}{100}*Y = 900$$ No Information about y or x hence unsufficient. "(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.
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Re: On a certain date, Hannah invested $5,000 at x percent [#permalink] ### Show Tags 22 Aug 2012, 14:05 1 Alexmsi wrote: The answer is (E). The Formula to calculate the interest is the following: $$\frac{x}{100}*X + \frac{y}{100}*Y = Interest$$ $$X + Y = 5000$$ "The total amount of interest earned by Hannah's two investments in one year was$900."

$$\frac{x}{100}*(5000-Y) + \frac{y}{100}*Y = 900$$

No Information about y or x hence unsufficient.

"(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. Intern Joined: 19 Apr 2012 Posts: 25 Re: On a certain date, Hannah invested$5,000 at x percent [#permalink]

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22 Aug 2012, 14:19
Hello,

"On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest." So, she invested some money at x percent and another part at y percent. The two parts together are X and Y. X+Y = 5000. Manager Joined: 05 Mar 2012 Posts: 59 Schools: Tepper '15 (WL) Re: On a certain date, Hannah invested$5,000 at x percent [#permalink]

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22 Aug 2012, 14:24
Alexmsi wrote:
Hello,

"On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest." So, she invested some money at x percent and another part at y percent. The two parts together are X and Y. X+Y = 5000. But that's my beef, the question never says that the total amount invested equals 5,000. Intern Joined: 19 Apr 2012 Posts: 25 Re: On a certain date, Hannah invested$5,000 at x percent [#permalink]

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22 Aug 2012, 14:47
Ah, sorry, my mistake. But that doesen't change so much. It is still unsufficient.
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24 Aug 2012, 07:25
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. _________________ Intern Joined: 13 Nov 2015 Posts: 10 Re: On a certain date, Hannah invested$5,000 at x percent [#permalink]

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19 Dec 2015, 15:50
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.

Thanks!
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Re: On a certain date, Hannah invested $5,000 at x percent [#permalink] ### Show Tags 19 May 2016, 07:42 2 Bunuel 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.

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.

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Re: On a certain date, Hannah invested $5,000 at x percent [#permalink] ### Show Tags 18 Sep 2017, 03:47 1. I1+ I2=900 not sufficient 2. I1=(5000*6*1)/100=300 so I2=600 but there are two unknowns for I2 R=y% an the principle Not sufficient E Re: On a certain date, Hannah invested$5,000 at x percent   [#permalink] 18 Sep 2017, 03:47
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