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

It is currently 16 Aug 2018, 06:48

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|=|a-b|, then a*b must be equal to:

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

Hide Tags

Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 421
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

Show Tags

New post 05 Jan 2015, 06:49
I am not sure if the way I thought of the absolute value was correct, but here it is.

QUESTION: If |a+b|=|a-b|, then a*b must be equal to:

I thought that when there is an absolute value, we think of the "value" within it with no regards to the sign. So, I thought it could be:
a+b= a-b. If we move a to the other side, both a's get cancelled, which leads to b=-b. Moving -b to the other side it becomes 2b=0. So, b=0, which means that a*b must be equal to 0.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47924
Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

Show Tags

New post 05 Jan 2015, 07:07
pacifist85 wrote:
I am not sure if the way I thought of the absolute value was correct, but here it is.

QUESTION: If |a+b|=|a-b|, then a*b must be equal to:

I thought that when there is an absolute value, we think of the "value" within it with no regards to the sign. So, I thought it could be:
a+b= a-b. If we move a to the other side, both a's get cancelled, which leads to b=-b. Moving -b to the other side it becomes 2b=0. So, b=0, which means that a*b must be equal to 0.


You are missing the second case there.

If a+b and a-b have the same sign, then we'd have a+b = a-b --> b=0 --> ab=0;
If a+b and a-b have the opposite signs, then we'd have a+b = -(a-b) --> a=0 --> ab=0.
_________________

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

Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 421
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

Show Tags

New post 05 Jan 2015, 07:39
Thank you for explaining. I have gone through the absolute values, but they keep creating some confusion.
Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1167
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

Show Tags

New post 27 Mar 2018, 08:08
Quote:
If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2


niks18 Bunuel chetan2u pushpitkc

Let me know if below approach is correct:

|a+b| or |a-b| will always yield a positive value.
This is because a modulus always represents an ABSOLUTE distance
from number line.


So |a+b|=|a-b|
simplifies to
a + b = a - b
I can cancel a from both sides in all circumstances.
2b = 0 -> b = 0
or a*b = 0

Hope assumptions made by me are correct.
_________________

It's the journey that brings us happiness not the destination.

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6527
If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

Show Tags

New post 27 Mar 2018, 08:40
adkikani wrote:
Quote:
If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2


niks18 Bunuel chetan2u pushpitkc

Let me know if below approach is correct:

|a+b| or |a-b| will always yield a positive value.
This is because a modulus always represents an ABSOLUTE distance
from number line.


So |a+b|=|a-b|
simplifies to
a + b = a - b
I can cancel a from both sides in all circumstances.
2b = 0 -> b = 0
or a*b = 0

Hope assumptions made by me are correct.



Ans here will be either A or B or both are 0..
And this is why..
You cannot remove modulus this way, you do know if B is greater or A or they are NEGATIVE..
So square both sides, since both are modulus..
a^2+b^2+2ab=a^2+b^2-2ab.....
4ab=0..
So either A or B or both are 0
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1167
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

Show Tags

New post 27 Mar 2018, 08:46
chetan2u

Quote:
You cannot remove modulus this way, you do know if B is greater or A or they are NEGATIVE.


But we shall still always get END RESULT as positive on opening modulus.

|5| = 5

|- 5| = - (-5) = 5

Am I correct?
_________________

It's the journey that brings us happiness not the destination.

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6527
Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

Show Tags

New post 27 Mar 2018, 09:13
1
adkikani wrote:
chetan2u

Quote:
You cannot remove modulus this way, you do know if B is greater or A or they are NEGATIVE.


But we shall still always get END RESULT as positive on opening modulus.

|5| = 5

|- 5| = - (-5) = 5

Am I correct?


Yes you are correct..
But |5-3|=|3-5| does not mean 5-3=3-5... That is 2=-2??
So square the MODULUS to get rid of Modulus
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Re: If |a+b|=|a-b|, then a*b must be equal to: &nbs [#permalink] 27 Mar 2018, 09:13

Go to page   Previous    1   2   [ 27 posts ] 

Display posts from previous: Sort by

If |a+b|=|a-b|, then a*b must be equal to:

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

Events & Promotions

PREV
NEXT


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®.