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]

10 May 2010, 09:32

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

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

[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jul 2012, 05:17, edited 1 time in total.

Edited the question and added the OA.

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Re: DS4 [#permalink]

10 May 2010, 14:38

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

(1) m < n. No info about x. Not sufficient.
(2) x >0. No info about m and n. Not sufficient.

(1)+(2) As from the above two statements nominators and denominator of both fractions are positive, we can crossmultiply --> is \frac{m+x}{n+x}>\frac{m}{n} --> is (m+x)n>(n+x)m --> is mn+xn>mn+xm --> is x(n-m)>0 --> as x>0 and n>m, then x(n-m)>0 is true. Sufficient.

Answer: C.
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Re: DS4 [#permalink]

10 May 2010, 21:01

Bunuel wrote:

Did you score 60 in the Quant or are you working with the GMAC!!! :-)

Awesome dexterity in giving the solutions.

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

17 Jan 2013, 03:57

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LM wrote:

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

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

I used plug in...

1.
let m=3 and n=4 and x = 1
\frac{m}{n} = \frac{3}{4} while \frac{m+x}{n+x}= \frac{4}{5}
\frac{3}{4} < \frac{4}{5} YES!

let m=3 and n=4 and x=-1
\frac{m}{n} = \frac{3}{4} while \frac{m+x}{n+x}= \frac{2}{3}
\frac{3}{4} > \frac{2}{3} NO!

thus, INSUFFICIENT!

2. x > 0
From statement 1 we tested m=3 and n=4 and x=1 (see that x>0 here) and we got YES!

let m=4 and n=3
\frac{m}{n} = \frac{4}{3} while \frac{m+x}{n+x}= \frac{5}{4}
\frac{4}{3} > \frac{5}{4} NO!

thus, INSUFFICIENT!

Together, we combine and using statement 1 where when x>0 we get YES!

Answer: C

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

26 Feb 2013, 04:02

Why can't we cross multiply in the original statement?

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

26 Feb 2013, 04:07

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fozzzy wrote:

Why can't we cross multiply in the original statement?

Never multiply (or reduce) an inequality by variable (or by an expression with variable) if you don't know its sign.

We don't know whether n+x is positive or negative, thus don't know whether we should flip the sign or not.
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Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n? [#permalink] 26 Feb 2013, 04:07

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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?

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