Data Sufficiency

Is x a negative number?

(1) x^2 is a positive number
(2) x · |y| is not a positive number

please provide explanation. OA to follow after a few threads. Thanks.

just_do_it wrote:Is x a negative number?

(1) x^2 is a positive number
(2) x · |y| is not a positive number

please provide explanation. OA to follow after a few threads. Thanks.

Statement I
x^2 always will be positive. x can be negative or positive. Insufficient.

Statement II
x* lyl is not a positive, this means it could be 0 or negative. Because 0 is neither positive nor negative. Insufficient.

Combining I & II
if x^2 is positive, this means x is a non zero number. x*lyl will be negative. Therefore, x is negative. Sufficient.

Hence C.

OA?

E for me ,

1) X^2 is positive therefor x can be positive or negative

2) x.|y| is not a postive number , thus x can be 0 , -ve or +ve

it can be positive when |y| = 0,

combining X CAN BE +VE , -VE , thus E

I agree with the explanation given by parallel chase...The ans should be C...Whats the OA?

Sorry for the delay in posting the OA.

OA is E

just_do_it wrote:Is x a negative number?

(1) x^2 is a positive number
(2) x · |y| is not a positive number

(1) x can be anything except 0, so it could be + or -... insufficient.

(2) x*|y| is either negative or 0.

if y = 0, then x * |0| = 0 no matter what x is.
Therefore, if y = 0, x could be any number... insufficient.

Together: if y=0, then x could be + or -... still insufficient, choose (E).

Thanks Stuart!

Stuart Kovinsky wrote:

just_do_it wrote:Is x a negative number?

(1) x^2 is a positive number
(2) x · |y| is not a positive number

(1) x can be anything except 0, so it could be + or -... insufficient.

(2) x*|y| is either negative or 0.

if y = 0, then x * |0| = 0 no matter what x is.
Therefore, if y = 0, x could be any number... insufficient.

Together: if y=0, then x could be + or -... still insufficient, choose (E).

In (2), possibility that x*|y| is negative is not discussed. Can anyone elaborate it

I also have one question, what difference does mod make to the entire question..what would be the solution if b would have been just x*y is not positive

Thanks for your time and efforts !

In (2), possibility that x*|y| is negative is not discussed. Can anyone elaborate it

I also have one question, what difference does mod make to the entire question..what would be the solution if b would have been just x*y is not positive

Thanks for your time and efforts !

You are right; not positive means it could include 0 and negtaive. What Stuart pointed out is if its 0 (not positive) i.e. |y| is 0 then x could be negative or positive and still the product would not be positive. We dont have to get in to the realm of the product being negative

If it was x.y is not positive then still y could be 0(so we cant tell for sure if x is postive or negative). Still the answer would be E)