GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Oct 2018, 20:05

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

If a > b and if c > d , then which of the following must be

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

Hide Tags

Board of Directors
User avatar
P
Joined: 01 Sep 2010
Posts: 3304
If a > b and if c > d , then which of the following must be  [#permalink]

Show Tags

New post Updated on: 19 Mar 2012, 05:51
1
6
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

74% (01:09) correct 26% (01:36) wrong based on 332 sessions

HideShow timer Statistics

If a > b and if c > d , then which of the following must be true?

A. a-b > c+d
B. a-c > b-d
C. c+d < a-b
D. b+d < a+c
E. a-c < b+d

here the answer is E but i wonder if is incorrect because we add unequal quantities but should not be a + c > b+d ???

_________________

COLLECTION OF QUESTIONS AND RESOURCES
Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection - The Next Generation 3. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos
Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Reading-comprehension_Oldy but goldy question banks


Originally posted by carcass on 19 Mar 2012, 05:39.
Last edited by Bunuel on 19 Mar 2012, 05:51, edited 1 time in total.
Edited the question and the OA
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49968
Re: Inequality questions  [#permalink]

Show Tags

New post 19 Mar 2012, 05:49
3
4
carcass wrote:
If a > b and if c > d , then wich of the following must be true ??

1) a-b > c+d
2) a-c > b-d
3) c+d < a-b
4) b+d < a+c
5) a-c < b+d

here the answer is E but i wonder if is incorrect because we add unequal quantities but should not be a + c > b+d ???


You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

BACK TO THE ORIGINAL QUESTION:
If a > b and if c > d , then which of the following must be true?
A. a-b > c+d
B. a-c > b-d
C. c+d < a-b
D. b+d < a+c
E. a-c < b+d

Since the signs of the inequalities are in the same direction we can add them: \(a+c>b+d\), which is the same as the option D: \(b+d < a+c\). So, the correct answer is D, not E.

Answer: D.

Hope its' 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

General Discussion
Manager
Manager
avatar
Joined: 22 Feb 2012
Posts: 86
Schools: HBS '16
GMAT 1: 740 Q49 V42
GMAT 2: 670 Q42 V40
GPA: 3.47
WE: Corporate Finance (Aerospace and Defense)
GMAT ToolKit User
Re: If a > b and if c > d , then which of the following must be  [#permalink]

Show Tags

New post 19 Mar 2012, 05:58
I think answer E is wrong here.

Is a > b and if c > d , then wich of the following must be true ??

1) a-b > c+d
2) a-c > b-d
3) c+d < a-b
4) b+d < a+c
5) a-c < b+d

so i picked 100 > 1 and 3 > 2 to test E

100-3<1+2 (FALSE)

I think D is answer
Board of Directors
User avatar
P
Joined: 01 Sep 2010
Posts: 3304
Re: Inequality questions  [#permalink]

Show Tags

New post 19 Mar 2012, 07:02
Bunuel wrote:
carcass wrote:
If a > b and if c > d , then wich of the following must be true ??

1) a-b > c+d
2) a-c > b-d
3) c+d < a-b
4) b+d < a+c
5) a-c < b+d

here the answer is E but i wonder if is incorrect because we add unequal quantities but should not be a + c > b+d ???


You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

BACK TO THE ORIGINAL QUESTION:
If a > b and if c > d , then which of the following must be true?
A. a-b > c+d
B. a-c > b-d
C. c+d < a-b
D. b+d < a+c
E. a-c < b+d

Since the signs of the inequalities are in the same direction we can add them: \(a+c>b+d\), which is the same as the option D: \(b+d < a+c\). So, the correct answer is D, not E.

Answer: D.

Hope its' clear.



Infact Bunuel as you can see from my question above I pick the right answer D but something make me suspicious and I thought to ask here to you.


This shows how is important to rely solely and exclusively on good gmat material.

Thanks Mod.
_________________

COLLECTION OF QUESTIONS AND RESOURCES
Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection - The Next Generation 3. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos
Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Reading-comprehension_Oldy but goldy question banks

Intern
Intern
avatar
Joined: 11 Jul 2012
Posts: 41
Re: If a > b and if c > d , then which of the following must be  [#permalink]

Show Tags

New post 31 Oct 2012, 11:47
1
Algebraic Approach
a>b ==> a-b>0 (1)
c>d ==> c-d>0 (2)
(1) + (2) ==> a-b + c-d > 0 (a+c) -(b+d)>0 ==> (b+d) < (a+c)
Intern
Intern
avatar
Joined: 24 Mar 2014
Posts: 36
Location: United States
GMAT 1: 700 Q50 V35
WE: Project Management (Computer Software)
If a>b and c<d, which of the following MUST be true?  [#permalink]

Show Tags

New post 31 Jul 2015, 10:54
If a>b and c<d, which of the following MUST be true?
a)a−d>c−b
b)a+d>b
c)b+c>a−d
d)b−d<a−c
e)a2+d2>b2+c2
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12660
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a > b and if c > d , then which of the following must be  [#permalink]

Show Tags

New post 31 Jul 2015, 16:01
Hi All,

To address the original prompt....In questions that include inequalities in this fashion, it's important to note that we know NOTHING about how A and B relate to C and D. For example, it could be that A is the biggest number, but it might be second biggest (behind C) or third biggest (behind C and D). As such, what MUST be true will likely involve combining the bigger variables from each pair and the smaller variables in each pair.

Since A > B and C > D, adding A and C will lead to a sum that MUST be greater than the sum of B and D.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8447
Premium Member
Re: If a > b and if c > d , then which of the following must be  [#permalink]

Show Tags

New post 03 Apr 2018, 09:30
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

GMAT Club Bot
Re: If a > b and if c > d , then which of the following must be &nbs [#permalink] 03 Apr 2018, 09:30
Display posts from previous: Sort by

If a > b and if c > d , then which of the following must be

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.