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# If m>0 and n >0, is ((m+x)/(n+x)) > (m/n)

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If m>0 and n >0, is ((m+x)/(n+x)) > (m/n) [#permalink]

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09 Mar 2010, 20:49
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If m>0 and n >0, is ((m+x)/(n+x)) > (m/n)

(1) m<n
(2) x>0

Thanks!
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09 Mar 2010, 21:39
I say C

First we look at statement 1, and choose some numbers to plug in and test.
2 for M, and 3 for N.
If we plug in 2 for X, then 4/5 > 2/3
If we plug in -2 for X, then 0/1 < 2/3
Since it can't be solved we cross out A and D

Then we look at statement 2, and choose some numbers to plug in and test.
I've kept X as 2
If M=2 and N=3 then it works as 4/5 > 2/3
But remember to forget statement 1
What if M=3 and N=2, then 5/4 < 3/2
So B doesn't work either.

However if you combine the 2 statements together you see that you do have enough information to solve, therefore the answer is C. Hope that was helpful. And feel free to visit gmat.sg for additional help on your GMAT preparation.
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10 Mar 2010, 00:17
metallicafan wrote:

If m>0 and n >0, is ((m+x)/(n+x)) > (m/n)

(1) m<n
(2) x>0

Thanks!

st 1) m/n is always positive as m and n are both > 0 and as m < n, there is a chance depending on the value of x that m+x could be negative and n+x could be positive or both are positive or both are negative.
m = 4, n = 6, x = - 5 ... NO
NOT sufficient

st 2) x>0
now as all 3 variables are positive, all the expressions in the numerator and denominator are positive and the equation can be reduced to

((m+x)/(n+x)) > (m/n)
(m+x) * n > (n+x) * m
mn + xn > mn + xm
x * (n-m) > 0
either x>0 and n-m > 0 OR x< 0 and n-m<0
x > 0 and we dont know if n>m .
not sufficient

Combining both
we know n>m and x>0 .. so yes

C

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10 Mar 2010, 13:29
If m>0 and n >0, is ((m+x)/(n+x)) > (m/n)

(1) m<n
(2) x>0

1.) if m=2 and n=3
((2+x)/(3+x)) > (2/3). x value required = Insuff

2.) using question stem m>0 and n>0 & x>0
when m=2 & n=3 & x=4 = yes
when m=3 & n=2 & x=4 = no

Using (1) & (2) Sufficient. Hence "C"

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Re: Algebra question   [#permalink] 10 Mar 2010, 13:29
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