Inequalities- concept

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."

Quote

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

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

"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

Quote

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

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

Quote

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

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

Attachments

Quote

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

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

Please check the Solution of a Quadratic Inequation.

Attachments

Quote

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

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

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Quote

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

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."

Quote

Post new topic Post Reply

• Page 1 of 1

5/5

5 Star (473 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review