ABSOLUTE VALUE YES/NO DS

cramya wrote:Is |X-1| < 1 ?

1) (x-1)^2 <= 1

2) x^2 - 1 > 0

Source: 2008 GMAT Club

OA:E

I think its [spoiler]B)[/spoiler](The reason being if its equal to or greater we can answer the question with a definite NO which makes it SUFFICIENT)


Comments/feedback welcome!

Is |X-1| < 1 ?

When will this be true?

Well, if x is between 0 and 2, we'll get a yes.

Every other value will give us a no.

(1) (x-1)^2 <= 1

x = 1.5 fits this rule and gives us a "yes" answer.
x = 2 fits this rule and gives us a "no" answer.
Insufficient!

(2) x^2 - 1 > 0

x = 1.5 fits this rule and gives us a "yes" answer.
x = 2 fits this rule and gives us a "no" answer.
Insufficient.

Together:

we can still choose both 1.5 and 2, so we can still get both a "yes" and a "no"... choose (E), not enough information.

Remember, we don't have to pick integers!

Thanks so much again!

Remember, we don't have to pick integers!

This is hurting me from time and again! I am thinking this post hopefully reinstills the consideration of non integers in a DS when no info on x is given

Stmt II

I simplified

x^2>1
|x|>1

x>1 x<-1

Considered just integers which led me to B).

So going back to my question if x was given to be an integer would B) be the right choice?


Thanks Stuart!!!!!!

Cramya ,Please see if this works

From 1 x^2 -2x+1 <= 1
x^2 -2x<=0
x^2<= 2x-- A

Not sufficient

From 2 x^2>1 => -x^2 < -1---B
Not sufficient

Add A and B => 0<=2x-1
2x>=1
x>=1/2

X=1/2 will satisfy the question, X=3 won't ..

So E