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N is an integer. Is N negative ?

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N is an integer. Is N negative ?  [#permalink]

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New post 18 Jun 2013, 15:49
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N is an integer. Is N negative ?

(1) |N| = -N
(2) N^4 = N^2
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Re: N is an integer . Is N negative ?  [#permalink]

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New post 18 Jun 2013, 15:56
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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]

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New post 18 Jun 2013, 17:56
1
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]

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New post 18 Jun 2013, 17:59
1
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]

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New post 18 Jun 2013, 18:33
1
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]

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New post 18 Jun 2013, 18:51
1
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]

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New post 12 Aug 2017, 05:42
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guerrero25 wrote:
N is an integer. Is N negative ?

(1) |N| = -N
(2) N^4 = N^2


1) |N| = -N
=> N ≤ 0
=> N could be 0, -1, -2,...
Insufficient.

2) \(N^4\) = \(N^2\)
=> N = -1, 0, 1
Insufficient.

1+2)
N could be 0 or -1.
Insufficient.

E is the answer.
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Re: N is an integer . Is N negative ?  [#permalink]

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New post 18 Jun 2013, 17:51
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]

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New post 18 Jun 2013, 18:32
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]

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New post 18 Jun 2013, 18:43
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]

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New post 18 Jun 2013, 18:48
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]

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New post 27 Jun 2013, 16:15
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)
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Re: N is an integer. Is N negative ?   [#permalink] 27 Jun 2013, 16:15
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