Is |x-1| <1?
Since Absolute value function is always non negative, we can square both sides,
We get is (x-1)^2<1?
Statement 1 is (x-1)^2< = 1
If (x-1)^2<1: answer to question is yes
(x-1)^2= 1: hence answer is No,
So Statement 1 is NOT SUFFICIENT.
Statement2: Question stem (x-1)^2<1?
Can be reduced to is x(x-2)<0
Or is 0<x<2
Now St2: x^2-1>0 gives x >1 or x <-1
Now x can be -2, answer to question stem is No
Or 1.5 answer to question stem is yes.
Hence NOT SUFFICIENT.
Combining both Statement 1 & 2, we get
X can be 2, answer to question stem- NO
Or 1.5 answer to question stem is yes.
Hence Answer E
Buttercup3 wrote:
Bunuel wrote:
13. Is |x-1| < 1?
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0
Last one.
Is |x-1| < 1? Basically the question asks is 0<x<2 true?
(1) (x-1)^2 <= 1 --> x^2-2x<=0 --> x(x-2)<=0 --> 0<=x<=2. x is in the range (0,2) inclusive. This is the trick here. x can be 0 or 2! Else it would be sufficient. So not sufficient.
(2) x^2 - 1 > 0 --> x<-1 or x>1. Not sufficient.
(1)+(2) Intersection of the ranges from 1 and 2 is 1<x<=2. Again 2 is included in the range, thus as x can be 2, we cannot say for sure that 0<x<2 is true. Not sufficient.
Answer: E.
Still not clear on this one.
Can you please explain why is 1 insufficient I am not able to eliminate 1 also why is not C sufficient?
Thanks in Advance