Inequalities

[divya23]

IF M>0 AND N>0 ,IS M+X/N+X>M/N
1.M<N
2.X>0

ANS = BOTH

we can here solve d inequality
n(m+x)>m(n+x)
nm+nx>mn+mx
nx>mx
n>m
is the approach right then why is one not the ans??

[Frankenstein]

Hi,
You cannot cross multiply in inequalities because we do not know the sign of x which can change the sign of n+x because in doing so, we are effectively multiplying both sides by n(n+x). We know that n>0 but we do not know the sign of (n+x). If n+x is positive the inequality holds. If it is negative, the inequality changes.
Is M+X/N+X>M/N ?
We need to check: Is m+x/n+x-m/n > 0?
m+x/n+x-m/n = [(m+x)n - m(n+x)]/n(n+x) = x(n-m)/n(n+x)
From(1): m<n. So, n-m>0. But we do not know the sign of x/(n+x)
Not Sufficient
From(2): x>0. But we do not know the sign of (n-m)/(n+x)
Not Sufficient
Both(1)&(2) : n-m >0, n>0, x>0, n+x>0
So, x(n-m)/n(n+x) > 0
Sufficient

Hence, C

[amit2k9]

M+x / N+x > M/N gives (MN+Nx-MN-MX)(N+x)*N > 0 x(N-M)/(N+x)*N > 0

a N>M tells nothing about x here. Not sufficient.

b x>0 tells nothing about N-M. not sufficient.

a+b means both numerator and denominator positive. C it is.

[vaibhavdoshi]

The Inequality holds true for all values of M,N when X is positive.

IMO B

[Brent@GMATPrepNow]

This question is essentially testing our knowledge of the following rule:

If we take a fraction with positive numerator and denominator, and we increase the numerator and denominator by the same amount, then the value of the fraction approaches (i.e., gets closer to) 1

Examples:
If we take 1/2 and increase the numerator and denominator by 3, we get 4/5
Notice that 4/5 is closer to 1 than 1/2 is

Similarly, if we take 3/2 and increase the numerator and denominator by 3, we get 6/5
Notice that 6/5 is closer to 1 than 3/2 is.

So, if we begin with a fraction greater than 1, then adding a positive number to numerator and denominator will decrease the value of the fraction, and if we begin with a fraction less than 1, then adding a positive number to numerator and denominator will increase the value of the fraction.

Statement 1 ensures that the initial fraction (M/N) is less than 1, but it does not ensure that we are adding a positive value to the numerator and denominator. INSUFFICIENT

Statement 2 ensures that we are adding a positive value to the numerator and denominator, but it does not tell us whether the initial fraction (M/N) is greater than or less than 1. INSUFFICIENT

The statements combined ensure both. SUFFICIENT

So the answer is C

Cheers,
Brent

[kevincanspain]

We can also simplify the question: intead of a > b, we can rewrite the question as a - b >0 and get a common denominator:

(m+x)/(n+x) - m/n = x(n - m)/n(n+x) > 0 ?