Is x positive?

Question

Is x positive?

(1)  x*|x|=x^2

(2)  x^2*|x|=x^3

Self made

broall · Answer

(1) $x\times |x| = x^2 \implies x(x-|x|)=0$

Hence $x=0$ or $x=|x| \implies x \geq 0$. 
In all cases, we have $x \geq 0$, insufficient.

(2) $x^2 \times |x| = x^3 = x^2 \times x \implies x^2 (|x|-x)=0$

Hence $x^2=0\implies x=0$ 
or $x=|x| \implies x\geq 0$
In all cases, we have $x \geq 0$. Insufficient.

Combine (1) and (2), we still have $x \geq 0$. Insufficient.

The answer is E.

chetan2u · Answer

Very important to NOT miss out all possible values of x- integer, fraction, positive , negative ,0 etc
70% gone wrong means we tend to OVERLOOK 0 as a value..

(1)  x*|x|=x^2 
x is surely non-negative BUT it can be 0 or positive
Insuff

(2)  x^2*|x|=x^3 
again x can be positive or 0
insuff

combined x can still be o, ans will be NO
x can be positive, ans will be YES
insuff

E

GMATBusters · Answer

What is the need of considering fraction/integer ?

Statement 1 : it shows that x is non negative, it can be 0 or any positive number.
Statement 2: it shows that x is non negative, it can be 0 or any positive number.
Statement 1 & 2 : it shows that x is non negative, it can be 0 or any positive number.
hence it is not sufficient that x is positive

GMATBusters · Answer

you are right, sometimes we make mistakes just because we take x as integers.
Thank you.

RohitSaluja · Answer

Both the equation given in the stimulus holds true when x>=0 so E is the answer

Is x positive?

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Is x positive?

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