Confused by solution

[heyvishy]

I saw a solution to a DS problem , which is confusing me.

Question:If x is not equal to 0, is |x| less than 1?
(1) x/|x| < x
(2) |x| > x

Actua lAnswer : Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

MY answer : 1 alone sufficient , 2 is not.
I thought , the option 1 alone was sufficient to solve the problem.

Reason : x/|x| < x
=>x < x |x| (multiplying both sides by |x|)
=> |x| > 1 (dividing both sides by x since x!=0)
hence proved.

but the solution says otherwise.
I understand the line of reasoning given in its solution ( i will share that later)
but what i do not understand is ,
"WAT is WRONG in my approach"
Can someone please....enlighten me ?

[Harbinder]

while solving inequalities we cannot cross multiply variables unless we know their sign.
So in this case in this case we need to find |x| < 1 or in other terms is 0<x<1 ?

Stmt1 is true when x > 1 and when -1<x<0 e.g (-1/2)
which doesn't give us a unique answer.

Stmt2 is true when x is -ve ...so both statements together tell us that x is between -1 and 0 which is < 1 ....
so IMO answer should be c

[mehravikas]

IMO - C

Statement 1 -

Let x = 2, therefore 2 / 2 < 2 - True
Let x = -1/2, therefore -1/2 * 2/1 < -1/2 - True

Not sufficient

Statement 2 -

Let x = -2, therefore |-2| > -2 - True
Let x = -1/2, therefore |-1/2| > -1/2 - True
Let x = 2, therefore |2| > 2 - False

Not Sufficient

combining 1 and 2 you get x = - 1/2