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(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.

(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.

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

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

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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 cross-multiply. (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.

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 cross-multiply. (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.

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

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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(n-m) > 0 ?

Now St 1 only: 1. m < n We don't know anything abt x to answer our new re-phrased 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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