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N is an integer. Is N negative ?

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N is an integer. Is N negative ? [#permalink] New post 18 Jun 2013, 14:49
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N is an integer. Is N negative ?

(1) |N| = -N
(2) N^4 = N^2
[Reveal] Spoiler: OA
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Re: N is an integer . Is N negative ? [#permalink] New post 18 Jun 2013, 14:56
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N is an integer . Is N negative ?

A) |N|= -N
That is true if N\leq{0}
Not sufficient to say that is negative (could be 0).

B) N^4=N^2
N^4-N^2=0 N^2(N^2-1)=0 so N could be 0,1 or -1.
Not sufficient

1+2) N could still be 0 or -1. Not sufficient
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Re: N is an integer . Is N negative ? [#permalink] New post 18 Jun 2013, 16:51
This may be a silly question but could you go over #1 in a bit more depth?

Thanks!

Zarrolou wrote:
N is an integer . Is N negative ?

A) |N|= -N
That is true if N\leq{0}
Not sufficient to say that is negative (could be 0).

B) N^4=N^2
N^4-N^2=0 N^2(N^2-1)=0 so N could be 0,1 or -1.
Not sufficient

1+2) N could still be 0 or -1. Not sufficient
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Re: N is an integer . Is N negative ? [#permalink] New post 18 Jun 2013, 16:56
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WholeLottaLove wrote:
This may be a silly question but could you go over #1 in a bit more depth?

Thanks!



|N|= -N

If N>0 then N=-N or N=0 but since 0 is not in the interval >0, this is not a valid solution.

If N\leq{0} then -N=-N and is always true (-n always equal -n).

So the original |N|= -N tells us that N\leq{0}.

Hope it's clear
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Re: N is an integer . Is N negative ? [#permalink] New post 18 Jun 2013, 16:59
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WholeLottaLove wrote:
This may be a silly question but could you go over #1 in a bit more depth?

Thanks!

Zarrolou wrote:
N is an integer . Is N negative ?

A) |N|= -N
That is true if N\leq{0}
Not sufficient to say that is negative (could be 0).

B) N^4=N^2
N^4-N^2=0 N^2(N^2-1)=0 so N could be 0,1 or -1.
Not sufficient

1+2) N could still be 0 or -1. Not sufficient


This is basics of absolute value:

|x|=-x when x\leq{0}.
|x|=x when x\geq{0}.
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Re: N is an integer . Is N negative ? [#permalink] New post 18 Jun 2013, 17:32
Wait, why does N = 0?


Zarrolou wrote:
WholeLottaLove wrote:
This may be a silly question but could you go over #1 in a bit more depth?

Thanks!



|N|= -N

If N>0 then N=-N or N=0 but since 0 is not in the interval >0, this is not a valid solution.

If N\leq{0} then -N=-N and is always true (-n always equal -n).

So the original |N|= -N tells us that N\leq{0}.

Hope it's clear
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Re: N is an integer . Is N negative ? [#permalink] New post 18 Jun 2013, 17:33
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WholeLottaLove wrote:
Wait, why does N = 0?



If N>0 then N=-N or 2N=0 or N=0 but since 0 is not in the interval >0, this is not a valid solution.
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Re: N is an integer . Is N negative ? [#permalink] New post 18 Jun 2013, 17:43
Got it, thanks. I was getting confused because of the similarity between this and the other question I had!

Zarrolou wrote:
WholeLottaLove wrote:
Wait, why does N = 0?



If N>0 then N=-N or 2N=0 or N=0 but since 0 is not in the interval >0, this is not a valid solution.
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Re: N is an integer. Is N negative ? [#permalink] New post 18 Jun 2013, 17:48
A) |N|= -N
That is true if N\leq{0}
Not sufficient to say that is negative (could be 0).

I hate to ask one more stupid question but...

How is |n| = -n if n≤0? If n is zero then wouldn't |n| just be n, as opposed to -n?
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Re: N is an integer. Is N negative ? [#permalink] New post 18 Jun 2013, 17:51
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WholeLottaLove wrote:
A) |N|= -N
That is true if N\leq{0}
Not sufficient to say that is negative (could be 0).

I hate to ask one more stupid question but...

How is |n| = -n if n≤0? If n is zero then wouldn't |n| just be n, as opposed to -n?


Given |N|= -N, if N=0 you get |0|=-0 which still holds true ( 0=0 )
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Re: N is an integer. Is N negative ? [#permalink] New post 27 Jun 2013, 15:15
N is an integer. Is N negative ?

(1) |N| = -N
-N is equal to an absolute value which means it must be positive. So, -N = -(-N). However, N can also equal zero as |0| = -0 is valid. N ≤ 0 but we can't be sure if N is negative or not.
INSUFFICIENT

(2) N^4 = N^2
N^4 = N^2 when n = -1, 0, 1. Again we can't tell if N is positive, zero or negative.

1+2) 1) tells us that n is zero or negative and 2) tells us that n is negative or zero or positive. Therefore, N could be negative or zero.
INSUFFICIENT

(E)
Re: N is an integer. Is N negative ?   [#permalink] 27 Jun 2013, 15:15
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