mustu wrote:
Is |x| < 1 ?
(1) |x + 1| = 2|x – 1|
(2) |x – 3| > 0
As I have said before, most mod questions are best tackled using a number line. You don't need to do many calculations then.
|x| means the distance from 0.
|x-3| means the distance from 3.
etc. For details of this approach, check out:
Let's go on to this question now.
Is |x| < 1 i.e. Is the distance of point x from 0 less than 1?
Statement 1: |x + 1| = 2|x – 1|
This means 'distance of x from -1 is twice the distance of x from 1'. Draw the number line now. There will be 2 points where the distance from -1 will be twice the distance from 1.
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For one of these points, distance from 0 is less than 1, for the other it is more than 1. So not sufficient.
Statement 2: |x – 3| > 0
This statement tells us that distance of x from 3 is more than 0 i.e. x does not lie at 3. It can lie anywhere else.
You can look at it in another way: Mods are always more than or equal to 0. All this statement tells us is that this mod is not equal to zero i.e. x is not equal to 3.
For some of these points, distance from 0 will be less than 1, for the others it will be more than 1. So not sufficient.
Using both statements together, statement 1 says that x is either 3 or a point between 0 and 1 (which I don't really need to calculate). Statement 2 tells us that x is not 3. So together, x must be a point between 0 and 1 and its distance from 0 must be less than 1. Sufficient.
Answer C.