OG10-qn- 256

[kishokbabu]

If m>0 & n>0, then (m+x)/(n+x) > m/n

1) n>m
2) x >0
As per OG answer it is mentioned that both statements are reqd to answer. The answer choice is C. But why the statement 1 alone cannot be sufficient to answer this qn

(m+x) / (n+x) > m/n
Multiply both sides by n+x ,then by n, then the statement becomes n(m+x) > m(n+x) = nm+nx> mn+mx

Now subtracting mn on both sides, it becomes nx > mx,
Divide by x on both sides it becomes n>m

Hence statement 1 is sufficient, pls explain why this is is not possible.

[sam2304]

If m>0 & n>0, then (m+x)/(n+x) > m/n

1) n>m
2) x >0
As per OG answer it is mentioned that both statements are reqd to answer. The answer choice is C. But why the statement 1 alone cannot be sufficient to answer this qn

(m+x) / (n+x) > m/n
Multiply both sides by n+x ,then by n, then the statement becomes n(m+x) > m(n+x) = nm+nx> mn+mx

Now subtracting mn on both sides, it becomes nx > mx,

we don't know whether x is +ve or -ve so we have to consider two cases from the above step while dividing.
If x is positive then n > m as explained by you.
If x is negative then n < m as dividing by -1 needs the inequality to be changed.

So we need the 2nd statement to prove n > m. Hope you get where you go wrong now:)

[GMATGuruNY]

If m>0 & n>0, then (m+x)/(n+x) > m/n

1) n>m
2) x >0
As per OG answer it is mentioned that both statements are reqd to answer. The answer choice is C. But why the statement 1 alone cannot be sufficient to answer this qn

(m+x) / (n+x) > m/n
Multiply both sides by n+x ,then by n, then the statement becomes n(m+x) > m(n+x) = nm+nx> mn+mx

Now subtracting mn on both sides, it becomes nx > mx,
Divide by x on both sides it becomes n>m

Hence statement 1 is sufficient, pls explain why this is is not possible.

Please note the portions highlighted in red.
Your solution assumes that n+x and that x itself are positive.
If n+x<0, then the calculations that follow the first highlighted step are invalid.
If x<0, then the calculation that follows that the second highlighted step is invalid.

But given that x>0 -- the information provided by statement 2 -- we can rephrase the question stem, since all of the unknowns are positive:
(m+x)/(n+x) > m/n
mn + xn > mn + xm
xn > xm
n > m?

Statement 2 enables us to rephrase the question stem: Is n>m?
Statement 1 provides the answer: n>m.
Thus, the two statements combined are SUFFICIENT.

The correct answer is C.

[ArunangsuSahu]

PROPERTIES of fractions..

All of m,n and x have to be available for the inference

Hence (C)