Data Sufficiency

Is x a negative number?

(1) x2 is a positive number.

(2) x × |y| is not a positive number.


OA - E

Is x a negative number?

(1) x2 is a positive number.
Insufficient. x can be either positive or negative and still satisfy this statement. x cannot equal 0.
x=1, x2=1
x=-1, x2=1

(2) x X |y| is not a positive number.
Insufficient.
x can be either negative or 0.

(1) and (2)
From (1), x is either positive or negative. x is not 0.
From (2), x is either negative or 0.
Combined, x is negative.

IMO C

I noticed the OA is E. Where am I going wrong? Thanks.

deepak123gmat wrote:Is x a negative number?

(1) x2 is a positive number.

(2) x × |y| is not a positive number.


OA - E

rephrase: x<0?

(1) x^2 = positive.
square of negative = positive. square of positive = positive
so x can either be positive or negative. Insufficient

(2) x * |y| <= 0 (warning as i'm reading: not a positive number can include 0 or negative number)
absolute value of a number (y) is always >= 0

if y = 0, |0| = 0 so x can be positive, negative or 0
if y = +, x can be 0 or negative
INSUFFICIENT

(1+2) from (1) x is either positive or negative. then from (2) x can be positive, negative or 0.........

so x can still be positive or negative

so i think the answer is E


[edit] i originally got C but thats because i omitted the possibility of x being positive in statement 2
.... yay 30 minutes later....

hi guys, my modest note
what if y=0 ( the value is not fixed), then x*|0|<=0, and (-x)*|0|<=0, and also (+x)*|0|<=0 the only we know that x=\=0
as x^2>0
so E seems reasonable answer

wahooza wrote:
[edit] i originally got C but thats because i omitted the possibility of x being positive in statement 2
.... yay 30 minutes later....

Thanks, wahooza... This is my error also...