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## GMAT Prep Question

##### This topic has expert replies
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### GMAT Prep Question

by agkrause » Tue Jul 27, 2010 4:06 pm
I was hoping someone could help me with the following DS question:
If m>0 and n>0, is (m+x)/(n+x) > m/n

1) m<n
2) x>0

Any help would be greatly appreciated. Thank you.

-agk

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by selango » Tue Jul 27, 2010 9:17 pm
m>0
n>0

(m+x)/(n+x)>m/n or n(m+x)>m(n+x)

stmt1,
m<n

we dont know abt X

Insuff

stmt2,
x>0

we dont know abt m and n

Insuff

Combining 1 and 2

m<n and x>0

m=2,n=4,x=2

n(m+x)>m(n+x)

m=1,n=2,x=-2

n(m+x)<m(n+x)

Insuff

Pick E
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by agkrause » Tue Jul 27, 2010 10:37 pm
Thank you for the reply. The test prep software actually says that the answer is C. I think that I may have figured it out, but I'm wondering if there's a more efficient way to figure it out. Below is my logic of how the answer may be C.

1) if m<n then m=2; n=4; 2+x/4+x is greater than 2/4 when x = 1, but not greater than 2/4 when x = 0 or -1.

Insufficient

2) x>0; if m=2; n=4; x=1; then m+x/n+x > m/n
but if m=4; n=2; x=1; then 5/3 < 4/2 and m+x/n+x < m/n

Insufficient

Combined = Sufficient: Together we can prove that when m<n and x>0 that m+x/n+x>m/n . I think that this is how they get the answer; unfortunately GMAT prep doesn't provide explanations.

agk

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by prep_to_lead » Wed Jul 28, 2010 7:46 am
This is how I went about:
Question:
If m>0 and n>0, is (m+x)/(n+x) > m/n
1) m<n
2) x>0

Before I jumped in I made solved the question.
Since I know m and n both are +ve, so I can cross multiply m and n in the question.
So,
the question becomes,
Is (m+x)/(n+x)> m/n?
Is n(m+x)>m(n+x) ?
Is nm + nx > mn + mx ?
cancel out mn from both sides, gives us

Is nx > mx ?

Now St 1 only:
1. m < n We don't know anything abt x to answer our new prephased question. Insuff.

Stmt 2 only:
2. X> 0 relation beteween m and n not known. So Insuff.

Now combined,
We know x > 0 i.e +ve and m < n so nx > mx answer is yes.

You can test values here too now to confirm,
x = 1, n = 3, m= 2, so nx > mx is 1.3 > 2.1 ie. 3>2 so yes.

So if x was -ve . i.e x< 0 then the inequality would have been revered. So both the stmts combined are suff.

Hope that helps.

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by agkrause » Wed Jul 28, 2010 9:15 am
Thank you for the response. I saw that you could cross multiply to set up the equation as n(m+x) > m(n+x), but I wasn't sure if that was possible, because if X<0, then you may be forced to multiply by a negative in the inequality, which would force you to flip the signs.k

agk

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