Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)
[#permalink]
Show Tags
24 Jul 2015, 01:13
3
Bunuel wrote:
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.
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
_________________
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)
[#permalink]
Show Tags
24 Jul 2015, 02:59
1
Bunuel wrote:
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.
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.
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)
[#permalink]
Show Tags
26 Jul 2015, 11:49
1
1
Bunuel wrote:
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.
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). _________________
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)
[#permalink]
Show Tags
09 Sep 2016, 13:25
Top Contributor
Bunuel wrote:
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.
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
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)
[#permalink]
Show Tags
10 Sep 2016, 03:21
Bunuel wrote:
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.
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.
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)
[#permalink]
Show Tags
11 Sep 2016, 13:07
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 wrote:
Bunuel wrote:
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.
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).
_________________
When you are grateful - when you can see what you have - you unlock blessings to flow in your life
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)
[#permalink]
Show Tags
12 Sep 2016, 03:25
1
1
DaenerysStormborn wrote:
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 wrote:
Bunuel wrote:
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.
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).
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).
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)
[#permalink]
Show Tags
01 Oct 2016, 20:42
Bunuel wrote:
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.
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
close
45% (01:40) correct 
