I have been there done that! Er, been where? Done what?!? Caught up getting most of Inequalities &/or absolute value questions wrong and going absolutely mad about it.
Here is some interesting thing I found out today. Inequalities and absolute values are best solved by imagination. Not like the ones where you imagine Luke Skywaker zooming through the Empire, but like the one that has axis and is called number lines. Well, that’s enough marketing for what I am about to tell. Let’s get down to business!
Absolute value is nothing but modulus. Heck! I know that, tell me something more! Ok, so here is a thing Modulus is the distance between Zero and that NUMBER. Yup, you probably knew that as well! But, are you using it to your advantage?
Take for example. |x-1|; the value of (x-1) lies between -1 and 1 on the number line. Therefore if, X should lie between 0 and 2 because X lies one step ahead of X-1. So just move your line. Simple as that.
Shall we test the absolute simplicity of the concept?
(1) -s<;=r; Says R lies between S and -S inclusive. Insufficient
(2) |r|>;=s ===>; Says R lies beyond S and -S inclusive. Insufficient.
Combine those two. We get, R can be -S or S. =>; Insufficient. Therefore, E.
Get that? Its that simple.
Shall we try a bit tougher one? How about this:
(1) |x| >; |y|
(2) |x-y| ;|x-y| =>; Remember Modulus is distance from Zero to a number. In what all cases, will cumulative distance between x and o and y and zero be greater than distance between x and y where, x and y are some number? Only if they are in the same side of the axis.. Simply put, This question is asking if x and y have same signs or not.
(1) |x| >; |y| ==>; Nope, this doesn’t tell me about their signs. Insufficient.
(2) |x-y| ; Ah, get back to number line. in what cases is Distance between x and y ; Awesome, exactly what we are looking for. Hence, B.
Please free too go through GMATCLUB.COM posts such as this to get more practice.