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N is an integer. Is N negative ? [#permalink]
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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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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) \(N^4=N^2\) \(N^4N^2=0\) \(N^2(N^21)=0\) 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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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) \(N^4=N^2\) \(N^4N^2=0\) \(N^2(N^21)=0\) 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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18 Jun 2013, 17:56
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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]
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18 Jun 2013, 17:59



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Re: N is an integer . Is N negative ? [#permalink]
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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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18 Jun 2013, 18:33
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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]
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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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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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18 Jun 2013, 18:51
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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]
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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)




Re: N is an integer. Is N negative ?
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