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If Z is an integer, what is the value of Z ?

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If Z is an integer, what is the value of Z ? [#permalink] New post 26 Dec 2012, 19:45
If Z is an integer, what is the value of Z ?

(1) Z^2 <= 0
(2) Z^3 <= 0

I thought that if i can solve from (1), then i can also solve from (2). So, I selected D which is incorrect.
Please help me in understanding why we cannot solve from (2).

Thanks & Regards
Vinni
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Re: If Z is an integer, what is the value of Z ? [#permalink] New post 26 Dec 2012, 22:54
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vinnik wrote:
If Z is an integer, what is the value of Z ?

1. Z^2 <= 0
2. Z^3 <= 0

I thought that if i can solve from (1), then i can also solve from (2). So, I selected D which is incorrect.
Please help me in understanding why we cannot solve from (2).

Thanks & Regards
Vinni

In STAT1 its sufficient because minimum value of square of a number is 0(if the number itself is zero). Square of any number will always be greater than or equal to zero. So, only possible value if z which satisfies both z>=0 and z<=0 is z=0 so. It's sufficient.

STAT2: since its z^3 <= 0 then z can be 0 or any negative value as cube of negative number is negative. So we have infinitely many solutions to this.

So, answer wil be A
Hope it helps!
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Re: If Z is an integer, what is the value of Z ? [#permalink] New post 27 Dec 2012, 08:58
nktdotgupta wrote:
In STAT1 its sufficient because minimum value of square of a number is 0(if the number itself is zero). Square of any number will always be greater than or equal to zero. So, only possible value if z which satisfies both z>=0 and z<=0 is z=0 so. It's sufficient.

STAT2: since its z^3 <= 0 then z can be 0 or any negative value as cube of negative number is negative. So we have infinitely many solutions to this.

So, answer wil be A
Hope it helps!


Thanks Ankit.
Appreciate your reply.

Regards
Vinni
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Re: If Z is an integer, what is the value of Z ? [#permalink] New post 03 Jan 2013, 09:08
Given the two peices of data look at it this way;

An integer can either be negative, positive or zero.

Any number N that is squared has to be positive. Any number N that is cubed can either be negative or zero.

Only A gives you a definite answer - N must be 0
Re: If Z is an integer, what is the value of Z ?   [#permalink] 03 Jan 2013, 09:08
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