OG10-qn- 256

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 62
Joined: Wed May 04, 2011 9:50 pm
Thanked: 2 times
Followed by:2 members

OG10-qn- 256

by kishokbabu » Thu Jan 12, 2012 5:36 am
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.
Source: — Data Sufficiency |

User avatar
Legendary Member
Posts: 1239
Joined: Tue Apr 26, 2011 6:25 am
Thanked: 233 times
Followed by:26 members
GMAT Score:680

by sam2304 » Thu Jan 12, 2012 5:44 am
kishokbabu wrote: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:)
Getting defeated is just a temporary notion, giving it up is what makes it permanent.
https://gmatandbeyond.blogspot.in/

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Jan 12, 2012 6:28 am
kishokbabu wrote: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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Master | Next Rank: 500 Posts
Posts: 382
Joined: Thu Mar 31, 2011 5:47 pm
Thanked: 15 times

by ArunangsuSahu » Thu Jan 12, 2012 7:22 am
PROPERTIES of fractions..

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

Hence (C)