This is how I went about:
Question:
If m>0 and n>0, is (m+x)/(n+x) > m/n
1) m<n
2) x>0
Before I jumped in I made solved the question.
Since I know m and n both are +ve, so I 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 ?
Now St 1 only:
1. m < n We don't know anything abt x to answer our new prephased question. Insuff.
Stmt 2 only:
2. X> 0 relation beteween m and n not known. So Insuff.
Now combined,
We know x > 0 i.e +ve and m < n so nx > mx answer is yes.
You 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 suff.
Hope that helps.
