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

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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 ]
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 ]
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 sufficient1+2) N could still be 0 or -1. Not sufficient

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Re: N is an integer . Is N negative ? [#permalink ]
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 ]
18 Jun 2013, 16:59
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Senior Manager

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

VP

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Re: N is an integer . Is N negative ? [#permalink ]
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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Kant , Critique of Pure Reason

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Senior Manager

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