It is currently 18 Oct 2017, 12:10

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Inequality involving absolute values

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Intern
Joined: 25 Jul 2007
Posts: 46

Kudos [?]: 43 [0], given: 0

Inequality involving absolute values [#permalink]

### Show Tags

08 Nov 2007, 17:14
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

Kudos [?]: 43 [0], given: 0

VP
Joined: 10 Jun 2007
Posts: 1434

Kudos [?]: 350 [1], given: 0

Re: Inequality involving absolute values [#permalink]

### Show Tags

08 Nov 2007, 17:35
1
KUDOS
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

There will be two solutions to this...
a>0, b>0
Ans: a>b

a>0, b<0
Ans: a>-b

a<0, b>0
Ans: -a<b => a>-b, which is same as #2

a<0, b<0
Ans: -a<-b => a>b, which is same as #1

Kudos [?]: 350 [1], given: 0

Intern
Joined: 25 Jul 2007
Posts: 46

Kudos [?]: 43 [0], given: 0

Re: Inequality involving absolute values [#permalink]

### Show Tags

08 Nov 2007, 19:26
bkk145 wrote:
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

There will be two solutions to this...
a>0, b>0
Ans: a>b

a>0, b<0
Ans: a>-b

a<0, b>0
Ans: -a<b => a>-b, which is same as #2

a<0, b<0
Ans: -a<-b => a>b, which is same as #1

For the second part of the solution, when a<0, b>0 shouldn't the equation be -a>b instead of -a<b as mentioned by you. If your equation holds then for a=-1 and b=2, |a|>|b| doesn't hold.

Kudos [?]: 43 [0], given: 0

VP
Joined: 10 Jun 2007
Posts: 1434

Kudos [?]: 350 [0], given: 0

Re: Inequality involving absolute values [#permalink]

### Show Tags

08 Nov 2007, 19:46
english_august wrote:
bkk145 wrote:
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

There will be two solutions to this...
a>0, b>0
Ans: a>b

a>0, b<0
Ans: a>-b

a<0, b>0
Ans: -a<b => a>-b, which is same as #2

a<0, b<0
Ans: -a<-b => a>b, which is same as #1

For the second part of the solution, when a<0, b>0 shouldn't the equation be -a>b instead of -a<b as mentioned by you. If your equation holds then for a=-1 and b=2, |a|>|b| doesn't hold.

Yep, you are absolutely right. Careless mistake on my part. You caught one mistake, I caught another of my own. There will be four solutions to
|a|>|b|

a>0, b>0
Ans: a>b

a>0, b<0
Ans: a>-b

a<0, b>0
Ans: -a>b => a<-b

a<0, b<0
Ans: -a>-b => a<b

Kudos [?]: 350 [0], given: 0

SVP
Joined: 29 Aug 2007
Posts: 2472

Kudos [?]: 842 [0], given: 19

Re: Inequality involving absolute values [#permalink]

### Show Tags

08 Nov 2007, 21:38
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

|a|>|b|

1. if a and b both are +ve: a > b.
2. if a and b both are -ve: a < b.
3. if a is +ve and b is -ve: a > b.
4. if a is -ve and b is +ve: a < b.

so we have two positions: 1. a > b and a < b

Kudos [?]: 842 [0], given: 19

CEO
Joined: 29 Mar 2007
Posts: 2554

Kudos [?]: 512 [0], given: 0

Re: Inequality involving absolute values [#permalink]

### Show Tags

08 Nov 2007, 22:27
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

if a>0 b>0

a>b

if a>0 and b<0>-b

if a<0 & b<0>-b --> a<b

if a<0>0

-a>b a<-b.

Kudos [?]: 512 [0], given: 0

Re: Inequality involving absolute values   [#permalink] 08 Nov 2007, 22:27
Display posts from previous: Sort by

# Inequality involving absolute values

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.