Because x could be zero.

I have the same question.

Taking each statement individually:

statement 1: if x^2 is positive, x could either be positive or negative. Not sufficient.

statement 2: if x · |y| is not a positive number, there would generally be two possible values for x. X could either be negative or x could be equal to 0. Not sufficient.

Taking the statements together: Taking the intersection between statement 1 (x could be positive or negative) and statement 2 (x could be negative or equal to 0), x can only be negative.

What's missing in this equation?

Is x a negative number?

(1) x2 is a positive number.

(2) x · |y| is not a positive number.


Stmt I

x= - 2 yes
x= 2 no

INSUFF

Stmt II

x .|y| no positive

x = 2 y=0 x.|y| = 0 which is not positive

x = -2 y=0 x.|y| = 0 which is not positive

INSUFF

Together:

x = 2 y=0 x.|y| = 0 which is not positive

x = -2 y=0 x.|y| = 0 which is not positive


Hence E

Dont forget : 0 is non positive and non negative.

Regards,
Cramya

Because x could be zero.

If we can determine x is zero then we can most defnitely answer the question x is not a negative number.

In this case x cant be zero since stmt I says x^2 is a positive number

Hope this helps!

Regards,
CR

cramya,
Thanks for the reply.

Please let me know dont we take common answer between I and II condition, I remeber doing that when we check +ve -ve or Abs values. If that is the case then in this question..

by I - X<0 or X>0
by II - X<0 or X=0

so cant we conclued that X<0 by these two statements?

Please help.

by II - X<0 or X=0

Welcome,

Why do u say must x be less than 0 or equal to 0 by stmt II?

Unless there is a typo in stmt II I dont see why

x .|y|

y can be 0 making x.|y| not positive.

x can be +ve, negative or 0 just considering stmt II.

When u consider stmt I and II still x can be positive or negative but not 0

Let me know if u still hv questions/concerns.

Regards,
CR

Thanks alot cramya, now it is clear to me.

Thanks a ton.

cramya, Can you please also advise me good source for such questins, I am done with OG and MGMAT guide. But still stuck on 48 due to DS. Please guide.

Thanks in advance.

Statement 1:
X can be positive as well as negative

Statement 2:
Since |y| is always positive
and so x*|y| is negative,
so x HAS TO be negative


Please correct me where I am wrong

"Since |y| is always positive
and so x*|y| is negative,
so x HAS TO be negative "

Thsi analysis is wrong for statemt II not positive means Negetive or zero.

cramya, Can you please also advise me good source for such questins, I am done with OG and MGMAT guide. But still stuck on 48 due to DS. Please guide

This forum has more questions that we can think of. I would search for absolute value/number properties/remainders/inequalities on this forum and try to solve them. Personaly I have found gmat club to be good for the most part($79.99)25 math tests(37 q each) and 6 verbal tests(41 q each)

I guess the more u practice (with takeaways for sure i.e quality+quantity) u will be able to add more trap lookouts to your arsenal.


Hope this helps!

Regards,
Cramya

Thanks alot Cramya, I'll follow that.