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

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

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.

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

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.

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

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?

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).

GMAT assassins aren't born, they're made,
Rich

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
_________________

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!

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...
_________________

Video solution from Quant Reasoning starts at 47:08
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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.

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.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com

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.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com