Problem Solving

Loan X has a principal of $10,000x and a yearly simple interest rate of 4%. Loan Y has a principal of $10,0000y 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. What's the value for x and a value for y corresponding to yearly simple interest rate of 5% for the consolidated loan. 

A. 21' 32
B. 32' 51
C. 32' 96
D. 64' 81
E. 64' 51

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

All values of x and y satisfying above equation, wud give 5% interest rate for the consolidated loan

From ans choices; Check C if it's typed correctly

x=96, y=32 could be the answer

teejaycrown wrote:Loan X has a principal of $10,000x and a yearly simple interest rate of 4%. Loan Y has a principal of $10,0000y 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 load. Make only two selections:

21
32
51
64
81
96

In the original problem -- from the IR section of one of the Preptests -- the answer choices appear in a table, as shown here.

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.
4%----------5%-------------------8%

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

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

Only X=96 and Y=32 yield the required ratio of 3:1.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

GMATGuruNY wrote:

teejaycrown wrote:Loan X has a principal of $10,000x and a yearly simple interest rate of 4%. Loan Y has a principal of $10,0000y 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 load. Make only two selections:

21
32
51
64
81
96

In the original problem -- from the IR section of one of the Preptests -- the answer choices appear in a table, as shown here.

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.
4%----------5%-------------------8%

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

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

Only X=96 and Y=32 yield the required ratio of 3:1.

Mitch - thank you so much for the elegant solution.

Is anyone going to address the fact that it can be solved algebraically?

given: r = (4x+8y)/(x+y), then...
rx+ry=4x+8y, thus
rx-4x=8y-ry, thus
x(r-4)=y(8-r), thus
x = [(8-r)/(r-4)] * y
given r=5: x=3y

Also, has anyone noticed that the only solution is when you don't treat r as a %? It should be .05 in a calculation, but the only answer comes when treating it as an integer. That's just bad math.