Data Sufficiency

Is x a negative number?

(1) x^2 is a positive number.

(2) x · |y| is not a positive number.


Here is a great question - I previously posted a question about negativity and I believe it was a learning experience for everyone. Here is a question that gives a great lesson, which is PAY ATTENTION TO THE DETAILS AND REPHRASE CORRECTLY.

The rephrase is not is a positive number but is x positive or O. Here is the trap. Lets all keep note of our boundary words!

statement 1 gives x as positive and negative. Hence insufficient
statement 2 gives x as negative or 0/
combining for choice c gives a common agreement on negative.

WHy isnt choice c correct?


qa e

simba12123 wrote:Is x a negative number?
(1) x^2 is a positive number.
(2) x · |y| is not a positive number.

x<0?

(1)
x^2 is a positive number
x<0, x>0 but x nit eq to 0
INSUFF

(2)
x · |y| is not a positive number.
x · |y| =< 0
if x · |y| = 0 then:
a. x=0, y=0
b. x=0, y = any value
c. x=any value, y =0

if x · |y| < 0 then:
d. x<0 because |y| > 0
INSUFF


(1)(2)
x not equal to zero from (1)
we have c and d from (2)
INSUFF

E

Do not forget about zero

A

Is not special...Its not sufficient since when square of x is positive, x cûd be positive or negative


B
x · |y| is not a positive number

means x · |y| is negative or x · |y| is 0

x · |y| is negative

|y| means y can be +Y or it could be -Y

If Y=+Y, Then to satisfy equation x · |y| is negative , x has to be negative

If Y=-Y, Then to satisfy equation x · |y| is negative , x has to be positive
Y=-X, X=positive only then equation is satisfied

This means we are not sure whether X is a negative no


x · |y| is 0


either of X or |y| or both have to be zero


x can be zero or positive or negative not sufficient


Hence, we cannot come to a Conclusion E