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# Conceptual Problem - Manhattan Advanced GMAT Q# 91

Author Message
Intern
Joined: 24 May 2012
Posts: 10
GMAT Date: 11-10-2013

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21 Sep 2013, 00:58
2
KUDOS
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)

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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

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25 Sep 2013, 02:54
1
KUDOS
Expert's post
arslano wrote:
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)

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

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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 29 Aug 2013 Posts: 77 Location: United States Concentration: Finance, International Business GMAT 1: 590 Q41 V29 GMAT 2: 540 Q44 V20 GPA: 3.5 WE: Programming (Computer Software) Re: Conceptual Problem - Manhattan Advanced GMAT Q# 91 [#permalink] ### Show Tags 25 Sep 2013, 05:28 arslano wrote: 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 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 $$\frac{x}{y}$$ = $$\frac{2mn}{(m-n)}$$ Intern Joined: 03 Feb 2011 Posts: 21 Re: Conceptual Problem - Manhattan Advanced GMAT Q# 91 [#permalink] ### Show Tags 26 Sep 2013, 13:01 Hi Karishma, What about this " If |x| != |y|, xy != 0, " why this was given Regards, lr Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7440 Location: Pune, India Re: Conceptual Problem - Manhattan Advanced GMAT Q# 91 [#permalink] ### Show Tags 26 Sep 2013, 21:44 1 This post received KUDOS Expert's post nitestr wrote: Hi Karishma, What about this " If |x| != |y|, xy != 0, " why this was given Regards, lr 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Conceptual Problem - Manhattan Advanced GMAT Q# 91   [#permalink] 26 Sep 2013, 21:44
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