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Loan X has a principal of $10,000x and a yearly simple interest rate o

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ksung84
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Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink] New post   Updated on: 16 Oct 2023, 02:15
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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
21
32
51
64
81
96
Submit
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Originally posted by ksung84 on 07 Aug 2013, 12:36.
Last edited by Sajjad1994 on 16 Oct 2023, 02:15, edited 5 times in total.
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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink] New post   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 interest rate o [#permalink] New post   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


Show 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 interest rate o [#permalink] New post   18 Dec 2015, 02:37
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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 interest rate o [#permalink] New post   27 Dec 2015, 10:24
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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 interest rate o [#permalink] New post   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 interest rate o [#permalink] New post   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 interest rate o [#permalink] New post   26 Sep 2016, 00:27
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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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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink] New post   Updated on: 02 Jul 2017, 09:52
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."

Thanks in advance!

Originally posted by harleen.kaur on 02 Jul 2017, 09:49.
Last edited by abhimahna on 02 Jul 2017, 09:52, edited 1 time in total.
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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink] New post   29 Mar 2021, 23:37
I have seen this pop up in interest rate problems in general... usually when I see percent, I think X/100

Why are we only equating 5 to 4x + 8y/ x + y rather than doing 5/100?

In other words, this application of PER CENT seems to apply only sometimes...
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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink] New post   02 May 2021, 19:34
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Video solution from Quant Reasoning starts at 47:08
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink] New post   26 Jun 2022, 13:11
Hi Ron, could you explain how you inferred "X brings down the average by 1, Y brings up the average by 3."? I don't quite understand how you got that, thanks.

VeritasPrepRon wrote:
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


Show 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 interest rate o [#permalink] New post   26 Jun 2022, 14:05
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Hi BritLee,

In this prompt, we're essentially looking to take a certain number of '4s' and a certain number of '8s' to get an average of 5. This can be thought of as a 'weighted average' question, since we'll need more 4s than 8s to hit that average. As an example:

If we have one 4 and one 8, then the average would be (4+8)/2 = 12/2 = 6. This is higher than what we're looking for, so we need more 4s to bring that average down.

The idea that Ron was trying to convey is that each '4' is 'one below' the average of 5 that we're looking for and each '8' is '3 above' the average that we're looking for, so we need to have enough '4s' to 'counter-act' the effect that one '8' has on the average. We can do that with three '4s' (since 3 x 'one below' = '3 below' - and this counters the '3 above' that an '8' creates. This ultimately means that the ratio of '4s' to '8s' is 3:1 - and we need corresponding values of X and Y that fit that relationship.

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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink] New post   09 Jul 2022, 15:03
Can someone please explain me the calculation procedure of (bellow)

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

B) 5x+5y=4x+8y

x=3y

what do you calculation do you for A) and then for B)

please and thank you
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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink] New post   27 Oct 2022, 15:35
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icognitoto wrote:
Can someone please explain me the calculation procedure of (bellow)

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

B) 5x+5y=4x+8y

x=3y

what do you calculation do you for A) and then for B)

please and thank you


Hi icognitoto,

The equation 5 = (4X + 8Y)/(X+Y) is provided in the original prompt. We can 'simplify' this equation in just a few steps. Here's how:

First, we multiply both sides of the equation by (X+Y). This will 'cancel out' the denominator on the 'right side' of the equation:

5(X+Y) = (4X + 8Y)
5X + 5Y = 4X + 8Y

Now, we can 'combine like terms' (we'll put the X's on the left and the Y's on the right):

5X - 4X = 8Y - 5Y
X = 3Y

This gives us the ratio of X to Y - and ultimately tells us that the value of X is three times the value of Y.

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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink] New post   21 Mar 2024, 12:13
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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.

­This is a MIXTURE problem.
A 4% loan (X) is being combined with an 8% loan (Y) to form a CONSOLIDATED loan of 5%.
To solve, we can use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS. 

Step 1: Plot the 3 percentages on a number line, with the two starting percentages (4% and 8%) on the ends and the goal percentage (5%) in the middle.
 X 4%-------------------5%-------------------8% Y 

Step 2: Calculate the distances between the percentages.
X 4%---------1--------5%---------3---------8% Y 

Step 3: Determine the ratio in the mixture. 
The required ratio of X to Y is equal to the RECIPROCAL of the distances in red. 
X:Y = 3:1.

Only X=96 and Y=32 yield the required ratio of 3:1.­
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Re: Loan X has a principal of $10,000x and a yearly simple interest rate o [#permalink]
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