m and n

[naveenhv]

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

1) m<n

2) x>0

[vineeshp]

OA C.

1)
Let m=1/3. n = 1/2, x =2
m/n = 2/3
(m+x)/(n+x) = 7/3 / 5/2 = 14/15 .
(m+x)/(n+x) > m/n

But m=5. n = 6 if x = -1
m/n = 5/6 = 0.83...

(m+x)/(n+x) = 4/5 = 0.8
(m+x)/(n+x) < m/n

Stmt 2:
x>0.
NS
But m=2. n = 3, x = 1
m/n = 2/3
(m+x)/(n+x) = 3/4
(m+x)/(n+x) > m/n

But m=3. n = 2, x = 1
m/n = 3/2
(m+x)/(n+x) = 4/3
(m+x)/(n+x) < m/n

Combining the two.
m<n
m/n <1.

So the conditions set in each other are cancelled out.

Hence sufficient.
C

I know you can take similar values in all cases during the exam. I just tried to illustrate with as many values as possible.