It is currently 21 Nov 2017, 05:35

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42280

Kudos [?]: 132894 [1], given: 12391

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

Show Tags

New post 24 Jul 2015, 00:55
1
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

47% (01:39) correct 53% (01:37) wrong based on 212 sessions

HideShow timer Statistics

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.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132894 [1], given: 12391

2 KUDOS received
Manager
Manager
User avatar
Joined: 26 Dec 2011
Posts: 120

Kudos [?]: 104 [2], given: 44

Schools: HBS '18, IIMA
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 24 Jul 2015, 02:13
2
This post received
KUDOS
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
_________________

Thanks,
Kudos Please

Kudos [?]: 104 [2], given: 44

Current Student
avatar
B
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1774 [0], given: 794

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 24 Jul 2015, 03:59
1
This post was
BOOKMARKED
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.

D is the correct answer.

Kudos [?]: 1774 [0], given: 794

Manager
Manager
User avatar
Joined: 08 Jul 2012
Posts: 50

Kudos [?]: 17 [0], given: 15

Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 24 Jul 2015, 07:44
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 = 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
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. - Thomas A. Edison

Kudos [?]: 17 [0], given: 15

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42280

Kudos [?]: 132894 [1], given: 12391

Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 26 Jul 2015, 12:49
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132894 [1], given: 12391

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1847

Kudos [?]: 2611 [0], given: 362

Location: Canada
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 09 Sep 2016, 14:25
Expert's post
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

Answer =
[Reveal] Spoiler:
D


RELATED VIDEOS



_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2611 [0], given: 362

Manager
Manager
avatar
B
Joined: 08 Nov 2015
Posts: 52

Kudos [?]: 10 [0], given: 11

Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 10 Sep 2016, 04:21
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.

Kudos [?]: 10 [0], given: 11

Intern
Intern
User avatar
Joined: 17 Jun 2016
Posts: 39

Kudos [?]: 10 [0], given: 105

Location: India
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 11 Sep 2016, 14:07
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

Kudos [?]: 10 [0], given: 105

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42280

Kudos [?]: 132894 [1], given: 12391

Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 12 Sep 2016, 04:25
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132894 [1], given: 12391

Manager
Manager
avatar
B
Joined: 18 Jun 2016
Posts: 105

Kudos [?]: 21 [0], given: 76

Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 700 Q49 V36
WE: Business Development (Computer Software)
GMAT ToolKit User Reviews Badge
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 01 Oct 2016, 21:42
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

So answer is D
_________________

If my post was helpful, feel free to give kudos!

Kudos [?]: 21 [0], given: 76

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15579

Kudos [?]: 283 [0], given: 0

Premium Member
Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) [#permalink]

Show Tags

New post 09 Oct 2017, 18:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Re: For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r)   [#permalink] 09 Oct 2017, 18:39
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.