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Loan X has a principal of $10,000x and a yearly simple interest rate o
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Updated on: 30 May 2024, 16:02
Updated on: 30 May 2024, 16:02
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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 \(r = \frac{4x+8y}{x+y}\). 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 |
| 21 | ||
| 32 | ||
| 51 | ||
| 64 | ||
| 81 | ||
| 96 |
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X: 96
Y: 32
Intern
Joined: 25 Jul 2012
Posts: 8
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Concentration: Finance, Entrepreneurship
Schools: Booth '16 (A) Stanford '16
GPA: 3.56
Re: Loan X has a principal of $10,000x and a yearly simple interest rate o
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07 Aug 2013, 14:49
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.
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.
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 309
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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o
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08 Aug 2013, 11:24
08 Aug 2013, 11:24
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Expert Reply
ksung84
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
Can someone please explain how to solve this?
..........X..........Y..........Value
(A)..............................21
(B)..............................32
(C)..............................51
(D)..............................64
(E)..............................81
(F)..............................96
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
