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OG 11 DS 143 - don't get it, PLEASE HELP

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OG 11 DS 143 - don't get it, PLEASE HELP

by vstraesser » Sat Jan 21, 2012 3:17 am
Hi guys,
I've been working on a problem for a while. I understand the reasoning of the OG 11, but I have my own 'strategy' and can't see why it doesn't work out.
I appreciate your help. Here's the question:

If m>0 and n>0, is m+x/n+x>m/n?
(1) m<0
(2) x>0

Alright, the way I tackle this it wo rewrite the stem:
m/n + x/x > m/n?

(1) Since the m/n's are equal, the question is: is the integer x/x positiv or negativ? We don't know, hence insufficient.
(2) Now, we have m/n on both sides, on the left side we add x/x. If this is a positive number - which we get from statement 2 - then obviously the left side is bigger.

What do I miss here?

Thanks guys, appreciate your help GMAT on Friday, getting kinda nervous here:)
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by GMATGuruNY » Sat Jan 21, 2012 4:27 am
If m>0 & n>0, is (m+x)/(n+x) > m/n?

1) n>m
2) x >0
Statement 1 should read as I have posted above -- n>m -- information that is crucial here.

If a constant is added to the numerator and the denominator of a fraction between 0 and 1, the resulting fraction is GREATER than the original:
1/2 --> (1+1)/(2+1) --> 2/3, which is greater than 1/2.

If a constant is added to the numerator and the denominator of an IMPROPER fraction that is greater than 1, the resulting fraction is SMALLER than the original:
2/1 --> (2+1)/(1+1) --> 3/2, which is smaller than 2/1.

Since statement 2 alone does not tell us whether m>n or n>m, it is INSUFFICIENT.
Combining the statements, we know that a constant (x) is being added to both the numerator and the denominator of m/n (a fraction between 0 and 1), implying that the resulting fraction (m+x)/(n+x) will be greater than the original.
SUFFICIENT.

The correct answer is C.

Algebraically:

Given that x>0 -- the information provided by statement 2 -- we can rephrase the question stem, since all of the values are positive:
(m+x)/(n+x) > m/n
mn + xn > mn + xm
xn > xm
n > m?
Statement 1 provides a definitive answer to this rephrased question: it says that n>m.
Thus, the two statements combined are SUFFICIENT.
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