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Senior Manager  Joined: 10 Apr 2012
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N is an integer. Is N negative ?  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 46% (01:12) correct 54% (00:54) wrong based on 144 sessions

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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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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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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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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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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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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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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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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
Senior Manager  Joined: 13 May 2013
Posts: 399
Re: N is an integer . Is N negative ?  [#permalink]

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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
Senior Manager  Joined: 13 May 2013
Posts: 399
Re: N is an integer . Is N negative ?  [#permalink]

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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.
Senior Manager  Joined: 13 May 2013
Posts: 399
Re: N is an integer. Is N negative ?  [#permalink]

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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?
Senior Manager  Joined: 13 May 2013
Posts: 399
Re: N is an integer. Is N negative ?  [#permalink]

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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, 16:15
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