Inequalities- concept

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ikaplan: Master | Next Rank: 500 Posts; Posts: 181; Joined: Fri Sep 04, 2009 12:06 pmFollowed by: 1 member; Thanked: 17 times

by ikaplan » Sun Jul 27, 2014 5:47 am

I am trying to keep a 'Paraphrase Sheet' for DS, and I ran across the following condition:

w^2>1

I am not good at inequalities, so if someone could explain the logic behind this statement that would be great.

My reasoning: w^2-1>0, (w-1)*(w+1)>0 so there are 2 solutions: w>1, w>-1 (

My question: Do I put AND or OR between solutions number 1 or 2? Any concrete example is more than welcomed.

Thank you~

"Commitment is more than just wishing for the right conditions. Commitment is working with what you have."

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Source: Beat The GMAT — Data Sufficiency | Sun Jul 27, 2014 5:47 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Jul 27, 2014 5:57 am

ikaplan wrote:I am trying to keep a 'Paraphrase Sheet' for DS, and I ran across the following condition:

w^2>1

I am not good at inequalities, so if someone could explain the logic behind this statement that would be great.

My reasoning: w^2-1>0, (w-1)*(w+1)>0 so there are 2 solutions: w>1, w>-1 (

My question: Do I put AND or OR between solutions number 1 or 2? Any concrete example is more than welcomed.

Thank you~

Red Highlighted part is the wrong Reasoning

We should be looking at the correct reasoning in this way

W^2 > 1

i.e. w^2-1>0,
i.e.(w-1)x(w+1)>0
Product of two numbers (w-1) and (w+1) is Greater than 0
i.e. Either Both are Positive
i.e. (w-1)>0 as well as (w+1)>0
i.e. (w)>1 as well as (w)>-1
i.e. w must be greater than 1 to satisfy both the conditions

Or Both are Negative
i.e. (w-1)<0 as well as (w+1)<0
i.e. (w)<1 as well as (w)<-1
i.e. w must be Lesser than -1 to satisfy both the conditions

Therefore the correct range of the values is
W<-1 or W>1

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Jul 27, 2014 6:01 am

ALTERNATELY YOU CAN ALSO THINK ABOUT THIS PROBLEM THIS WAY

W^2 > 1

Square of any number will be Greater than 1 only when the Absolute Value of the number is Greater than 1

i.e. /W/ > 1
i.e. Either W>1 or W<-1

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Jul 27, 2014 6:13 am

Please refer to the attached DS question whose statement 1 is of such a type that has been solved logically without algebraic calculations

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Jul 27, 2014 6:19 am

Please check the Solution of a Quadratic Inequation.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jul 27, 2014 6:37 am

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ikaplan: Master | Next Rank: 500 Posts; Posts: 181; Joined: Fri Sep 04, 2009 12:06 pmFollowed by: 1 member; Thanked: 17 times

by ikaplan » Sun Jul 27, 2014 6:56 am

Thank you for the links GMATGuruNY.

I really need to brush up and build on my skills for inequalities issues. I'll make sure to go over each link in great detail.

Thanks~

"Commitment is more than just wishing for the right conditions. Commitment is working with what you have."

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