For the integers m, n, r, and s, if m + n = 250 and m n, is (m – r)

Question

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

Kudos for a correct  solution .

balamoon · Accepted Answer

Solution -

Its given that, (m – r) > (s – n), which is equivalent to (m + n) > (r + s). So we need to determine the inequality holds true or false.

Stmt1  - 250 > r + s --> From the question m + n = 250, so the inequality m + n > r + s is true. Sufficient.

Stmt2  - m + r + s = 375 --> We know that m + n = 250 and m > n, m must be greater than 125. Subtracting 125 from 375 yields 250, so if m is greater than 125, then r + s must be smaller than 250. So the inequality m + n > r + s is true. Sufficient.
ANS D

ENGRTOMBA2018 · Answer

Given, m>n, m+n=250 Question: is (m – r) > (s – n)? or is (m+n)>(s+r) ---> s+r<250 ? Statement 1 , sufficient to say yes fr s+r<250. Statement 2, m+r+s=375 ---> assuming (m – r) > (s – n) ---> m+n>375-m ---> 2m+n>375 or n >375-2m and n = 250-m Thus, 250-m > 375-2m --- m >125 Thus, if m+n = 250 and m >125 ---> m>n which is a give. Thus our assumption above of (m – r) > (s – n) holds TRUE. Thus this statement is sufficient as well. D is the correct answer.

JJo · Answer

given: m+n = 250 & m>n, hence n<125 & m>125

Asked: is (m-r)>(s-n), rearranging we get, is (m+n)>(s+r) ?

stmt1 : 250>r+s -->250 = m+n, hence m+n > r+s , sufficient

stmt2 : m+r+s = 375 -->r+s = 375-m, but m>125...so smallest possible value of m is 126 (m is given as integer)

so, r+s = 375-126 = 249 (this is max value of r+s) hence r+s is always equal to or less than 249 & m+n is 250 -->m+n > r+s....sufficient

Ans. D

Bunuel · Answer

800score Official Solution:

Statement (1) tells us that 250 > r + s. Since the question statement tells us that m + n = 250, we can determine that m + n > r + s.

Now, let us manipulate this inequality to see whether it is equivalent to the inequality in the question:
(m + n) > (r + s)
m > (r + s) – n
(m – r) > (s – n)

This is exactly what we were looking for. We can answer the question using Statement (1), hence it is sufficient.

Statement (2) tells us that m + r + s = 375.
Because we know that m + n = 250 and m > n, m must be greater than 125. Subtracting 125 from 375 yields 250, so if m is greater than 125, then r + s must be smaller than 250. We are now left with the same inequality that we were given in Statement (1), which can be manipulated to show that (m – r) > (s – n). So Statement (2) is also sufficient.

Since both statements are sufficient alone,  the correct answer is choice (D).

BrentGMATPrepNow · Answer

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

This is a great candidate for  rephrasing the target question . We have a video on this at the bottom of this post

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

RELATED VIDEOS
 https://www.youtube.com/watch?v=MyG1K3ee69w

https://www.youtube.com/watch?v=Od98BOicIq4

nayanparikh · Answer

From the question stem we have to prove that s+r< 250 
1. SUFFICIENT
2. m+r+s =375, m+n= 250 i.e. r+s=125+n, now it is given that m > n. So maximum value of n can be 124. Hence we use n=124 r+s would be 249 <250.
Hence SUFFICIENT
Correct answer is D.

DaenerysStormborn · Answer

Hello Bunuel,

I have a doubt. Please help me see what am I missing...

m, n, r, and s are integers-> nowhere it's mentioned that it is positive integer, it can as well be negative integer... in that case how can we reduce the equation (m – r) > (s – n) into (m + n) > (r + s)

thanks

Bunuel · Answer

We are concerned about the sign of a number when multiplying/dividing an inequality by that number. However we can safely add/subtract a number from both sides of an inequality, which is done in that example: add n+r to both sides of (m – r) > (s – n) to get (m + n) > (r + s).

Hope it's clear.

sidoknowia · Answer

To prove : m-r > s-n => m-r+n > s => m+n > s+r => 250 > s+r or s+r < 250 Also from the question stem m+n = 250 , m > n so maximum value for n can be 124 and minimum value of m can be 126 1. 250 > r+s ...... sufficient 2. m + r + s = 375 r + s = 375 - m lets take minimum value of m ie 126 as this will give us maximum value of r+s r + s = 375 - 126 => r + s = 249 => r + s < 250 This is also sufficient So answer is D

MsInvBanker · Answer

For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) > (s – n)?

(1) 250 > r + s

Rewriting  m-r > s-n

m+n > s+r

We know that m + n = 250

Thus,  250 > s+r

SUFFICIENT

(2) m + r + s = 375

m+n=250  and  m>n , we know that m is greater than 125.

375-125=250

As m is greater than 125,  r+s  has to be less than 250

Inequality stands true

SUFFICIENT.

Answer is  D

bumpbot · Answer

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For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)

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