If 2|x| + x^2 ≠ 0, what is the value of 1/2|x| + x^2?

Question

If  2|x|+x^2
eq{0} , what is the value of   \frac{1}{2|x|+x^2} ?

(1)  |x|=x^2

(2)  \frac{|x|}{x}>0

Chetan's question

gmat1393 · Answer

2|x|+x^2
eq{0} 
this implies  x
eq{0}

1 => x can be -1, 0 or 1 
since x cannot be 0 x can be -1 or 1
both the values give same result for   \frac{1}{2|x|+x^2}

2 =>  x >=1

IMO, Answer is A

QuantMadeEasy · Answer

Absolute Value of x is required

(1) possible values of x are -1 and 1. Sufficient

(2) |x|/x>0, x can be any positive number. Insufficient

IMO A

fireflyejd1 · Answer

Hey, I am confused about how you derived this part:
1 => x can be -1, 0 or 1
since x cannot be 0 x can be -1 or 1
can you please elaborate?

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