For the integers m, n, r, and s

[vipulgoyal]

For the integers m, n, r, and s, if m + n = 250 and m > n, is (m - r) > (s - n)?
(1) 250 > r + s
(2) m + r + s= 375

OE says the Qstem is asking
IS(m - r) > (s - n)
=
(m + n) > (r + s)
my query :- from stem we only get m is positive , or has minimum value 126 , we dont know the signs of n,r,and s , so how can these variables can be moved ether side without changing inequality(unless it would have given n, a and s are positive

[DavidG@VeritasPrep]

We only have to worry about the possibility that the inequality sign will flip when we're multiplying or dividing both sides of the inequality, not when adding or subtracting.

In this case, m- r > s -n is rewritten as m + n > s + r by adding r and n to both sides. Because we're only adding, not multiplying or dividing, we don't have to worry about the possibility of the inequality sign flipping.

[Brent@GMATPrepNow]

For the integers m, n, r, and s, if m + n = 250 and m > n, is (m - r) > (s - n)?
1) 250 > r + s
2) m + r + s = 375

Target question: Is (m - r) > (s - n)?

This is a great candidate for rephrasing the target question. We have a free video on this: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

If we take the inequality in the target question and add r and n to both sides, we get . . .
REPHRASED target question: Is (m + n) > (s + r)?

Since m + n = 250, we can also rephrase it this way . . .
REPHRASED target question: Is 250 > (s + r)?

Given Information: m + n = 250 and m > n
If m and n were EQUAL, then m and n would both equal 125
Since m is GREATER THAN n, we can conclude that m > 125

Statement 1: 250 > r + s
Perfect!
One of our REPHRASED target questions is Is 250 > (s + r)?
Since statement 1 allows us to answer the REPHRASED target question with certainty, it is SUFFICIENT

Statement 2: m + r + s = 375
Earlier (in the Given Information part of the solution), we determined that m > 125
So, we can reword statement 2 as: (a number bigger than 125) + (r + s) = 375
This means that (r + s) must be LESS THAN 250
In other words, 250 > (s + r)
One of our REPHRASED target questions is Is 250 > (s + r)?
Since statement 2 allows us to answer the REPHRASED target question with certainty, it is SUFFICIENT

Answer = D

Cheers,
Brent