Conceptual Problem - Manhattan Advanced GMAT Q# 91

Question

If |x| != |y|, xy != 0, 
x/(x+y) = n, and x/(x-y) = m,
then x/y = ?

what i do is, equate the two x and solve

x/(x+y) = n, and x/(x-y) = m, - equation (0)
x=nx+ny ; x=mx-my - equation (1)

on solving above
x/y=(m+n)/(m-n) - equation (2)

i now substitute values for m and n (3,2) and find the value for x/y. The value turns out to be 5.

But when i substitute the same values in the answer choices, none of the them match.

However, if i substitute the values (say 2,3 again) of x and y in equation (0) and find the corresponding values of m and n, and then substitute the values of m and n in the answer choices, the answer matches the value of x/y that i had chosen(2/3).

Im not able to understand why the answers are not matching x/y when i substitute random values of m,n straightaway in equation (2) and why they do so wen i substitute the values of m,n derived from the substituted values of x,y in equation(0)

Can someone please help in trying me understand where i am going wrong .

ANSWER CHOICES
a> 3m/2
b>3m/2n
c>n(m+2)/2
d>2nm/(m-n) This is the right answer
e>n^2-m^2/nm

KarishmaB · Answer

The problem is that you don't have independent values of m and n. These values are derived from the values of x and y. Depending on the values of x and y, we will get the values of m and n. Due to the relation between x/(x+y) and x(x-y), m and n cannot take every value.

Note that because m and n both depend on x and y, there will be certain relations between them. 
e.g. using each equation independently, you get 
x/y = n/(1 - n)
x/y = m/(m - 1)
Equating them, you get 2mn = m + n

When you take random values for m and n, these relations may not hold. So if you have to assume values, you have to assume values of the independent variables, not for the dependent variables.

So assume values for x and y and then proceed as shown below.
Say x = 2, y = 1
x/(x+y) = n = 2/3, and x/(x-y) = m = 2
You get x/y = (m+n)/(m-n) = (2+2/3)/(2 - 2/3) = 2
Put m = 2 and n = 2/3 in the options. Option (D) gives you 2.

shameekv · Answer

Well you are given,

\frac{x}{(x+y)} = n , and 
 \frac{x}{(x-y)} = m ,

First inverse the 2 equations,
 \frac{1}{n}  =  \frac{(x+y)}{x} 
 \frac{1}{m}  =  \frac{(x-y)}{x}

Subtract these 2 equations,
 \frac{1}{n}  -  \frac{1}{m}  =  \frac{(x+y)}{x}  -  \frac{(x-y)}{x} 
 \frac{(m-n)}{mn}  = 1 +  \frac{y}{x}  - 1 +  \frac{y}{x} 
 \frac{(m-n)}{mn}  = 2 \frac{y}{x} 
 \frac{(m-n)}{2mn}  =  \frac{y}{x}

Therfore  \frac{x}{y}  =  \frac{2mn}{(m-n)}

nitestr · Answer

Hi Karishma,

What about this " If |x| != |y|, xy != 0, " why this was given

Regards,

lr

KarishmaB · Answer

Yes, that's a good question. You should always analyze what the given data implies. 
It was necessary to give " If |x| != |y|, xy != 0, "

|x| != |y| implies that x is not equal to y. It also implies that x is not equal to -y. Note that we have x+y and x -y in the denominator. If either one of them is 0, the value of m or n will be undefined. Hence they need to give you that m and n have defined values. So x cannot be equal to y or -y.

Also we need to find the ratio of x/y. So y cannot be 0 either. xy != 0 implies that x is not 0 and y is not 0. So basically, they are telling us that values of m and n are defined and they are not 0. Also x/y is defined.

Conceptual Problem - Manhattan Advanced GMAT Q# 91

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