It is currently 21 Aug 2017, 16:35

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

If ab ≠ 0, is |a-b| > |a+b|?

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

Hide Tags

Top Contributor
Director
Director
User avatar
B
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 620

Kudos [?]: 708 [0], given: 58

Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

Show Tags

New post 07 Jan 2017, 09:07
Top Contributor
|a-b|>|a+b| will be true only when a and b have different signs, as when we are doing
-> |a-b| we are actually adding the values of a and b and
-> |a+b| we are actually subtracting the values of a and b.

STAT1
ab < 0 => a and b have different signs
SUFFICIENT

STAT2
a > b
a and b can have the same sign or can have different signs too
example:
1. a = 7 b = 2 => a> b
but |a-b|<|a+b| (|5| < |9|)
2. a = 7 b = -2 => a> b
|a-b|>|a+b| (|9| > |5|)
So, INSUFFICIENT

so, answer will be A
Hope it helps!
nayanparikh wrote:
If ab ≠ 0, is |a-b|>|a+b|?

1) ab < 0
2) a > b

Can any one please provide explanation on how to solve these type of questions ?
@Bunnel ?

_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Kudos [?]: 708 [0], given: 58

Intern
Intern
avatar
B
Joined: 18 Jan 2017
Posts: 40

Kudos [?]: 2 [0], given: 4

Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

Show Tags

New post 13 Mar 2017, 10:21
nayanparikh wrote:
If ab ≠ 0, is |a-b|>|a+b|?

1) ab < 0
2) a > b

Can any one please provide explanation on how to solve these type of questions ?
@Bunnel ?

Bunnel has already explained that squaring both the sides of this inequality is the easiest.

What I did was that for the following to be true:
|a-b|>|a+b|

Quick substitution of values tells us that the above inequality will be true only when a and b are of opposite signs. We can try a=1, b=-2 OR a=-2, b=1

So, the question basically is if a and b are of opposite signs.

(1) says ab < 0. This clearly means that b are of opposite signs. So sufficient.

(2) says a > b. This does not tell us that b are of opposite signs. So not sufficient.

Kudos [?]: 2 [0], given: 4

Manager
Manager
avatar
B
Joined: 13 Dec 2013
Posts: 172

Kudos [?]: 23 [0], given: 122

Location: United States
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Reviews Badge
If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

Show Tags

New post 15 Apr 2017, 11:12
Bunuel wrote:
If \(ab ≠ 0\), is \(|a-b| > |a+b|\)?

Square \(|a-b| > |a+b|\) (we can safely do this since both sides are nonnegative): is \(a^2 - 2ab + b^2 > a^2 +2ab + b^2\) --> is \(ab < 0\)?

(1) \(ab < 0\). Directly answers the question. Sufficient.

(2) \(a > b\). Not sufficient to say whether ab < 0.

Answer: A.



Hi Bunuel, to confirm, the sign of the sides matters because if we multiply by a -ve, then the inequality sign would need to flip, correct?

Kudos [?]: 23 [0], given: 122

Expert Post
1 KUDOS received
Math Expert
User avatar
D
Joined: 02 Sep 2009
Posts: 40995

Kudos [?]: 119127 [1] , given: 12015

Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

Show Tags

New post 15 Apr 2017, 11:17
1
This post received
KUDOS
Expert's post
Cez005 wrote:
Bunuel wrote:
If \(ab ≠ 0\), is \(|a-b| > |a+b|\)?

Square \(|a-b| > |a+b|\) (we can safely do this since both sides are nonnegative): is \(a^2 - 2ab + b^2 > a^2 +2ab + b^2\) --> is \(ab < 0\)?

(1) \(ab < 0\). Directly answers the question. Sufficient.

(2) \(a > b\). Not sufficient to say whether ab < 0.

Answer: A.



Hi Bunuel, to confirm, the sign of the sides matters because if we multiply by a -ve, then the inequality sign would need to flip, correct?


We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality).
For example:
\(2<4\) --> we can square both sides and write: \(2^2<4^2\);
\(0\leq{x}<{y}\) --> we can square both sides and write: \(x^2<y^2\);

But if either of side is negative then raising to even power doesn't always work.
For example: \(1>-2\) if we square we'll get \(1>4\) which is not right. So if given that \(x>y\) then we cannot square both sides and write \(x^2>y^2\) if we are not certain that both \(x\) and \(y\) are non-negative.


Check the link below for more:
Inequality tips
_________________

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 [?]: 119127 [1] , given: 12015

Intern
Intern
avatar
Joined: 14 Jun 2016
Posts: 4

Kudos [?]: 0 [0], given: 3

Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

Show Tags

New post 17 Apr 2017, 23:54
Bunuel wrote:
If \(ab ≠ 0\), is \(|a-b| > |a+b|\)?

Square \(|a-b| > |a+b|\) (we can safely do this since both sides are nonnegative): is \(a^2 - 2ab + b^2 > a^2 +2ab + b^2\) --> is \(ab < 0\)?

(1) \(ab < 0\). Directly answers the question. Sufficient.

(2) \(a > b\). Not sufficient to say whether ab < 0.

Answer: A.



Hai,
I am new here. I have a doubt. Where are the options mentioned, I don't see any A,B,C,D and E beneath the questions.

Kudos [?]: 0 [0], given: 3

Expert Post
Math Expert
User avatar
D
Joined: 02 Sep 2009
Posts: 40995

Kudos [?]: 119127 [0], given: 12015

Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

Show Tags

New post 18 Apr 2017, 02:11
subhash29 wrote:
Bunuel wrote:
If \(ab ≠ 0\), is \(|a-b| > |a+b|\)?

Square \(|a-b| > |a+b|\) (we can safely do this since both sides are nonnegative): is \(a^2 - 2ab + b^2 > a^2 +2ab + b^2\) --> is \(ab < 0\)?

(1) \(ab < 0\). Directly answers the question. Sufficient.

(2) \(a > b\). Not sufficient to say whether ab < 0.

Answer: A.



Hai,
I am new here. I have a doubt. Where are the options mentioned, I don't see any A,B,C,D and E beneath the questions.



This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.
_________________

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 [?]: 119127 [0], given: 12015

Intern
Intern
avatar
Joined: 14 Jun 2016
Posts: 4

Kudos [?]: 0 [0], given: 3

Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

Show Tags

New post 18 Apr 2017, 09:15
Bunuel wrote:
subhash29 wrote:
Bunuel wrote:
If \(ab ≠ 0\), is \(|a-b| > |a+b|\)?

Square \(|a-b| > |a+b|\) (we can safely do this since both sides are nonnegative): is \(a^2 - 2ab + b^2 > a^2 +2ab + b^2\) --> is \(ab < 0\)?

(1) \(ab < 0\). Directly answers the question. Sufficient.

(2) \(a > b\). Not sufficient to say whether ab < 0.

Answer: A.



Hai,
I am new here. I have a doubt. Where are the options mentioned, I don't see any A,B,C,D and E beneath the questions.



This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.

Thnx bunuel...

Sent from my A0001 using GMAT Club Forum mobile app

Kudos [?]: 0 [0], given: 3

Manager
Manager
User avatar
S
Joined: 15 Dec 2015
Posts: 102

Kudos [?]: 77 [0], given: 61

GMAT 1: 640 Q47 V31
GPA: 4
WE: Information Technology (Computer Software)
Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

Show Tags

New post 03 Aug 2017, 11:29

Kudos [?]: 77 [0], given: 61

Re: If ab ≠ 0, is |a-b| > |a+b|?   [#permalink] 03 Aug 2017, 11:29

Go to page   Previous    1   2   [ 28 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
11 Experts publish their posts in the topic Is 0 > ab? Bunuel 11 21 Aug 2016, 06:16
98 Experts publish their posts in the topic If ab ≠ 0, is ab > a/b ? gmatquant25 27 02 Feb 2017, 17:49
2 Experts publish their posts in the topic Is a/b > 0 ? carcass 6 13 Mar 2016, 08:41
6 Experts publish their posts in the topic Is ab > 0? banksy 6 22 Apr 2017, 09:28
2 Experts publish their posts in the topic Is a/b > 0? Creeper300 3 18 Jul 2016, 04:13
Display posts from previous: Sort by

If ab ≠ 0, is |a-b| > |a+b|?

  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®.