Inequalities- concept

[ikaplan]

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~

[GMATinsight]

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]

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

[GMATinsight]

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

[GMATinsight]

Please check the Solution of a Quadratic Inequation.

[GMATGuruNY]

These sorts of problems can be solved with the CRITICAL POINT approach.
Examples:
https://www.beatthegmat.com/inequality-c ... 89518.html
https://www.beatthegmat.com/knewton-q-t89317.html
https://www.beatthegmat.com/which-is-true-t89111.html
https://www.beatthegmat.com/inequalities ... 76123.html
https://www.beatthegmat.com/if-x-is-not- ... 65585.html
https://www.beatthegmat.com/inequality-q ... 74830.html
https://www.beatthegmat.com/if-x-is-posi ... 70254.html
https://www.beatthegmat.com/inequalities-t115175.html (2nd post)

[ikaplan]

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~