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gmat prep 2 question [#permalink] New post 12 Jun 2012, 13:09
Loan x has a principal of 10000x and a yearly simple interest rate of 4%. loan Y has a principal of $10000y and a yearly simple interest of 8%. Loans x and y will be consolidated to form loan Z with a principal of (10000x + 10000y) 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 load. make only two selections,

value x y
21
32
51
64
81
96

Dont know how to solve this question without T and E . Can someone explain the shortcut
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Re: gmat prep 2 question [#permalink] New post 12 Jun 2012, 16:45
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What are the correct answers? It seems to me that the answers are x=96 and y=32.

Here's the quick math: r is supposed to equal 5. You're given the formula for calculating r. r = (4x + 8y) / (x + y). Is that the correct formula? The original looks like the x+y is only under the 8y, not under the entire 4x + 8y. Anyway, let's just assume that the formula I wrote is correct. Just substitute 5 in for r and solve for x in terms of y.

5 = (4x + 8y) / (x + y). Multiply both sides by (x+y)
5x + 5y = 4x + 8y. Get x's on one side and y's on the other.
x = 3y. Look for answer choices in which one is triple another. Only 32 and 96 work.
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Re: gmat prep 2 question [#permalink] New post 13 Jun 2012, 02:41
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Here's my take:

4x+8y/(x+y) = 5
4x+8y = 5x + 5y
x = 3y

Choices:
21
32
51
64
81
96

Check lowest 3 choices:
21*3 = 63 (not in lower three choices; eliminated)
32*3 = 96 (present in lower three; RIGHT ANSWER)

Thus: x = 96 y = 32

(oops: error corrected!)

Last edited by macjas on 13 Jun 2012, 17:54, edited 2 times in total.
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Re: gmat prep 2 question [#permalink] New post 13 Jun 2012, 14:13
macjas wrote:
Here's my take:

4x+8y/(x+y) = 5
4x+8y = 5x + 5y
x = 3y

Choices:
21
32
51
64
81
96

Check lowest 3 choices:
21*3 = 63 (not in lower three choices; eliminated)
32*3 = 96 (present in lower three; RIGHT ANSWER)

Thus: x = 32 y = 96


Other way around, right? If x= 3y, x=96 and y =32.
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Re: gmat prep 2 question [#permalink] New post 02 Jul 2012, 00:47
Hey macjas then why this line is provided in the question "Loan x has a principal of 10000x and a yearly simple interest rate of 4%. loan Y has a principal of $10000y and a yearly simple interest of 8% " is of no use . Then why this line has been provided in the question ??just to confuse us !!


Pls reply !!
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Re: gmat prep 2 question [#permalink] New post 02 Jul 2012, 00:51
debabrata44 wrote:
Hey macjas then why this line is provided in the question "Loan x has a principal of 10000x and a yearly simple interest rate of 4%. loan Y has a principal of $10000y and a yearly simple interest of 8% " is of no use . Then why this line has been provided in the question ??just to confuse us !!


Pls reply !!


Exactly! It's of no use! This is one of the fundamental ways in which IR differs from the Q/V section of the GMAT. :-D IR is supposed to reflect 'real world' data; you need to figure out whether a data piece of data is relevant or not.
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Re: gmat prep 2 question [#permalink] New post 02 Jul 2012, 02:12
thanks a lot macjas !! :-D
Re: gmat prep 2 question   [#permalink] 02 Jul 2012, 02:12
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