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# Loan X has a principal of \$10,000x and a yearly simple inter

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Intern
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Loan X has a principal of \$10,000x and a yearly simple inter [#permalink]

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07 Aug 2013, 12:36
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Loan X has a principal of \$10,000x and a yearly simple interest rate of 4%. Loan Y has a principal of \$10,000y and a yearly simple interest rate of 8%. Loans X and Y will be consolidated to form Loan Z with a principal of \$(10,000x + 10,000y) and a yearly simple interest rate of r%, where r = (4x+8y)/(x+y). In the table, select a value for x and a value for y corresponding to a yearly simple interest rate of 5% for the consolidated loan. Make only two selections, one in each column.

..........X..........Y..........Value
(A)..............................21
(B)..............................32
(C)..............................51
(D)..............................64
(E)..............................81
(F)..............................96

[Reveal] Spoiler:
X=(F), Y=(B)

Can someone please explain how to solve this?

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Re: Loan X has a principal of \$10,000x and a yearly simple inter [#permalink]

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07 Aug 2013, 14:49
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You have X amount of 4% interest rate and Y amount of 8%. After consolidating these two deposits, the formula to find the new interest rate(r%) of the consolidated amounts is:

r= (4x+8y)/(x+y)

the problem indicates the new interest rate(r%) of the mix is 5%
substituting r with 5,we get:

5=(4x+8y)/(x+y)

5x+5y=4x+8y

x=3y

After you get the above equation, you just need to look at your options for an x that is 3 times of y.
Y=32 X=96

Hope my first post helps.

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Re: Loan X has a principal of \$10,000x and a yearly simple inter [#permalink]

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08 Aug 2013, 08:55
easy one....agree with the given solution....
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Re: Loan X has a principal of \$10,000x and a yearly simple inter [#permalink]

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08 Aug 2013, 11:24
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ksung84 wrote:
Loan X has a principal of \$10,000x and a yearly simple interest rate of 4%. Loan Y has a principal of \$10,000y and a yearly simple interest rate of 8%. Loans X and Y will be consolidated to form Loan Z with a principal of \$(10,000x + 10,000y) and a yearly simple interest rate of r%, where r = (4x+8y)/(x+y). In the table, select a value for x and a value for y corresponding to a yearly simple interest rate of 5% for the consolidated loan. Make only two selections, one in each column.

..........X..........Y..........Value
(A)..............................21
(B)..............................32
(C)..............................51
(D)..............................64
(E)..............................81
(F)..............................96

[Reveal] Spoiler:
X=(F), Y=(B)

Can someone please explain how to solve this?

This Integrated Reasoning Two-Part Analysis question can be broken down into a standard weighted-average question. Forgetting the 10,000 constant (which is only there to confuse you), you need to find the weighted average of x (4%) and y (8%) that comes up to 5%. The algebraic solution above is good, but you can also solve this through logic if you preferred. X brings down the average by 1, Y brings up the average by 3. Obviously there need to be more x's than y's, because the weighted average is closer to x. Hence we need 3 x's for every 1 y to end up at the weighted average given.

From there, you have to find answer choices that have a 3 to 1 ratio. Since there could be an infinite number of solutions, you know the GMAT will only give you one option among the answer choices that works. In this case 32 and 96. Again you need more x's than y's, so x is 96 and y is 32.

Quick takeaway here is that most of the concepts that you study for the GMAT are applied on the IR section as well. There isn't much new content to study (basically just graphics analysis), but sometimes you need to apply familiar concepts in new ways.

Hope this helps!
-Ron
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Re: Loan X has a principal of \$10,000x and a yearly simple inter [#permalink]

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18 Dec 2015, 02:37
ozhan wrote:
You have X amount of 4% interest rate and Y amount of 8%. After consolidating these two deposits, the formula to find the new interest rate(r%) of the consolidated amounts is:

r= (4x+8y)/(x+y)

the problem indicates the new interest rate(r%) of the mix is 5%
substituting r with 5,we get:

5=(4x+8y)/(x+y)

5x+5y=4x+8y

x=3y

After you get the above equation, you just need to look at your options for an x that is 3 times of y.
Y=32 X=96

Hope my first post helps.

NOW THAT NAILED IT. BY MERELY LOOKING AT THE QUESTION, WITHOUT SOLVING, YOU MIGHT NOTICE SOMETHING WITH 32 AND 98 AND 4 AND 8. BUT THEN YOU HAD TO SOLVE TO FIND OUT WHICH IS FOR WHICH SIDE.

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Re: Loan X has a principal of \$10,000x and a yearly simple inter [#permalink]

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27 Dec 2015, 10:24
lot of verbiage but as other have said easy, only thing to be solved that equation by setting it equal to 5%.
I agree with solution provided

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Re: Loan X has a principal of \$10,000x and a yearly simple inter [#permalink]

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31 Jan 2016, 12:35
Very simple after seeing the answer

I made the mistake to set up the equation as such:

4x+8y / x +y = .05

Can someone explain why you set r = 5 and not r = .05 in this case?

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Re: Loan X has a principal of \$10,000x and a yearly simple inter [#permalink]

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04 Feb 2016, 23:32
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Hi Frank22Times,

When deciding on how to represent an interest rate, you have to pay careful attention to what the prompt tells you.

If you were trying to calculate a basic interest, then you would almost certainly use a decimal point.

For example, 10% on a \$200 load is (.10)(\$200) = \$20

In this question though, we're told that a loan has an interest rate of R%. Notice how the % sign is already there - that means we should NOT use a decimal point. When we're told that R = (4x+8y)/(x+y), we're performing the specific calculation that's described in the prompt, so we need to use R=5 (and not R=.05).

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Re: Loan X has a principal of \$10,000x and a yearly simple inter [#permalink]

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26 Sep 2016, 00:27
Weighted averages method is the best way to approach this questions.

W1/W2 = (A2 - Average)/(Average - A1)

This gives the ratio to be 3:1

32 and 96
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02 Jul 2017, 09:49
I want to know the solution for the following question:-

"Loan X has a principal of \$10000X and a yearly simple interest rate of 4%. Loan Y has a principle of \$10000Y and a yearly simple interest of 8%. Loans X and Y will be consolidated to form Loan Z with a principle of \$(10000X + 10000Y) and a yearly SI of r%, where r=(4X+8Y)/(X+Y). what will be the value of X and Y corresponding to a yearly SI of 5% for the consolidated loan."

Last edited by abhimahna on 02 Jul 2017, 09:52, edited 1 time in total.
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# Loan X has a principal of \$10,000x and a yearly simple inter

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