Loan X has a principal of $x and a yearly simple interest rate of 4%.

Question

Loan X has a principal of $x and a yearly simple interest rate of 4%. Loan Y has a principal of $y and a yearly simple interest rate of 8%. Loans X and Y will be consolidated to form Loan Z with a principal of $(x + y) and a yearly simple interest rate of r%, where $r = \frac{4x + 8y}{x + y}$. 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.

ID: 100365

chetan2u · Answer

A question that can be easily solved in the least possible time frame by using weighted average method.

Now x is at 4% and y is at 8%, while the total amount x+y is at 5%, so in a way 5% is teh weighted average of 4 and 8.

Thus,  \frac{x}{y} = \frac{(8-5)}{(5-4)} = \frac{3}{1}

Look for options that give us values in 3:1 ratio.  Only 96000:32000

thesunnyguy · Answer

Official Explanation

Bismuth83 · Answer

1. We are given loan X and loan Y with principals $x and $y, respectively. We need to  find the possible values of the principals .

2. Let's start the problem with the equation that r = 5 instead of writing out the formulas for the loans. Then:

r = 5 \rightarrow \frac{4x + 8y}{x + y} = 5 \rightarrow 4x + 8y = 5x + 5y \rightarrow 3y = x

3. Looking at the answers, for x to be there then y needs to be either 21,000 or 32,000.

y = 21,000 \rightarrow x = 63,000 ,    which isn't in the answers   .

y = 32,000 \rightarrow x = 96,000 ,    which is in the answers   .

4. So, our answer is:  x = 96,000  and  y = 32,000 .

Dbrunik · Answer

okay, so i admittedly got this question wrong, but i think its a great question. heres why:

In TPA. there are going to be a lot of different options. here, you can test all the different cases until you come out with a 5. This is super intuitive because they present the formula to you. So, more or less anybody can just start plugging in values. this may work, but it will require a lot of time and testing to get it to work.

This is the key takeaway, these TPA problems that are testing weighted average or different variables, often are not wanting you to do more than a little bit of algebra. you need to simplify the equation given, and with that new information, determine some relationship with the variables, and you need to use the answer choices to help you solve.

cloudkim · Answer

Why x/y not y/x?
Thanks!

Bunuel · Answer

We are given:

$x is at 4% 
 $y is at 8% 
 $x + $y is at r = 5% (the weighted average rate)

Since the distance from the principal at 4% to the average rate (r) is 1, and the distance from the principal at 8% to r is 3, $x, the principal at 4%, must be larger than the principal at 8%, $y, to pull the average rate closer to 4%. Since the ratio of these distances is 1:3, the ratio of the principals $x to $y must be the inverse, 3:1.

Loan X has a principal of $x and a yearly simple interest rate of 4%.

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x	y
		21,000
		32,000
		51,000
		64,000
		81,000
		96,000

GMAT Two-part Analysis (TPA) Questions

Loan X has a principal of $x and a yearly simple interest rate of 4%.

Prep Toolkit

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More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards