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If m > 0 and n > 0, is (m+x)/(n+x) > m/n?
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Updated on: 30 Jul 2012, 05:17
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If m > 0 and n > 0, is (m+x)/(n+x) > m/n? (1) m < n. (2) x > 0.
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Originally posted by LM on 10 May 2010, 09:32.
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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Bunuel wrote: 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 \(x(nm)>0\) > as \(x>0\) and \(n>m\), then \(x(nm)>0\) is true. Sufficient.
Answer: C. 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?
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17 Jan 2013, 03:57
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?
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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?
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26 Feb 2013, 04:07



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Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?
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02 May 2014, 19:24
Hi Bunuel,
Why isn't the answer B given that in the below steps, (2) gives us the same information as in (1)?
(2) Because we know that both m and n are positive and that x is positive, we can safely crossmultiply. (m+x)*n > (n+x)*m mn + xn > mn + xm xn > xm n > m Because we now know that n > m, we can use the same steps that you used for C to answer the question and only (2) will be sufficient to answer the problem. Please tell me where I am going wrong here.



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Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?
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03 May 2014, 00:17
LM wrote: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?
(1) m < n. (2) x > 0. Statement I is insufficient: Let us say m = 4 and n = 5 Is (4+x)/(5+x) > 4/5? (Take a hint from the second statement  Apply the negation test) (4  4)/(54) is not greater than 4/5 (4 + 5)/(5+5) is greater than 4/5 Statement II is not sufficient: (4 + 5)/(5+5) is greater than 4/5 (5 + 4)/(4 + 4) is not greater than 5/4 Combining is sufficient: m > n and x is positive Cross multiplying the inequality: (mn + nx) > mn + mx n > m which is true in statement I Hence answer is C.
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Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?
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03 May 2014, 04:50
TooLong150 wrote: Hi Bunuel,
Why isn't the answer B given that in the below steps, (2) gives us the same information as in (1)?
(2) Because we know that both m and n are positive and that x is positive, we can safely crossmultiply. (m+x)*n > (n+x)*m mn + xn > mn + xm xn > xm n > m Because we now know that n > m, we can use the same steps that you used for C to answer the question and only (2) will be sufficient to answer the problem. Please tell me where I am going wrong here. For (2) we don't know whether n>m. The question asks whether (m+x)/(n+x) > m/n. For (2) when you simplify the question becomes is n>m? This is not given, that;s exactly what we need to find out. Does this make sense?
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Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?
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03 May 2014, 06:55
Yes, I realize this now, and that with (1), we know that the answer to this question statement is Yes.
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Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?
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26 Jan 2017, 20:12
Since we know m and n both are +ve, so we 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 ? or Is x(nm) > 0 ? Now St 1 only: 1. m < n We don't know anything abt x to answer our new rephrased question. Insufficient. St 2 only: 2. X> 0 relation between m and n not known. So Insufficient. Now combined, We know x > 0 i.e +ve and m < n so nx > mx answer is yes. We 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 sufficient. Hence C.
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Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?
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