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Director
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anybody has a quick approach to this one for the value of N: [#permalink]
 22 Apr 2007, 11:33
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anybody has a quick approach to this one for the value of N:
|NтАУ|N+1||=|NтАУ2|
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SVP
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o If n+1 >= 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N - N -1| = |N-2|
<=> 1 = |N-2|
<=> N=3 or N = 1
o If n+1 =< 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N + N+1| = |N-2|
<=> |2*N+1| = |N-2|
<=> -(2*N+1) = -(N-2) as 2*N+1 < 0 and N-2 < 0
<=> N = -3
Thus, N = -3 or N=1 or N=3
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techjanson wrote: Fig wrote: o If n+1 >= 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N - N -1| = |N-2|
<=> 1 = |N-2|
<=> N=3 or N = 1
o If n+1 =< 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N + N+1| = |N-2|
<=> |2*N+1| = |N-2|
<=> -(2*N+1) = -(N-2) as 2*N+1 < 0 and N-2 < 0
<=> N = -3
Thus, N = -3 or N=1 or N=3 Excellent explanation. Thanks! Thanks to u 
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FIG: you are the abs, mod King
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VP
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Fig wrote: o If n+1 >= 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N - N -1| = |N-2|
<=> 1 = |N-2|
<=> N=3 or N = 1
o If n+1 =< 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N + N+1| = |N-2|
<=> |2*N+1| = |N-2|
<=> -(2*N+1) = -(N-2) as 2*N+1 < 0 and N-2 < 0
<=> N = -3
Thus, N = -3 or N=1 or N=3
Can you please explain the step in red color?
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SVP
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fresinha12 wrote: FIG: you are the abs, mod King Thanks ... I just hope it helps to clarify it
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SVP
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goalsnr wrote: Fig wrote: o If n+1 >= 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N - N -1| = |N-2|
<=> 1 = |N-2|
<=> N=3 or N = 1
o If n+1 =< 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N + N+1| = |N-2|
<=> |2*N+1| = |N-2|
<=> -(2*N+1) = -(N-2) as 2*N+1 < 0 and N-2 < 0
<=> N = -3
Thus, N = -3 or N=1 or N=3 Can you please explain the step in red color? Ok
In the second case, we have n+1 =< 0. Thus, we have |n+1| = -(n+1) : an absolute must always be positive or equal to 0.
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Director
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Himalayan wrote: anybody has a quick approach to this one for the value of N:
|NтАУ|N+1||=|NтАУ2| what does NтАУ and NтАУ2 mean here?
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Manager
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same question as above
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Manager
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Is there a quant guru that could explain this question in more depth? I don't understand the transition ... "If n+1 >= 0, then |NтАУ|N+1||=|NтАУ2| <=> |N - N -1| = |N-2|" Why? Thanks in advance, a
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Please kudos if my post helps.
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CEO
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Himalayan wrote: anybody has a quick approach to this one for the value of N:
|NтАУ|N+1||=|NтАУ2| I guess the symbol (-ve sign) has been changed into something else. The question should be as under: Quote: What is the value of N:
|N - |N+1||=|N - 2| Work out from the inside modulus The possibilities for : (1) If (N+1) >= 0 (2) If (N+1) <= 0 (1) If (N+1) >= 0 |N - N -1| = |N - 2| |-1| = |N - 2| 1 = |N - 2| N = 1 or 3 (2) If (N+1) <= 0 |N+N+1| = |N - 2| |2N+1| = |N - 2| (i) 2N +1 = N - 2 2N - N = - 3 N = -3 (ii) 2N +1 = N - 2 2N +1 = - N + 2 2N + N = 1 N = 1/3 (ii) - 2N -1 = - N + 2 -N = 3 N = -3 N = -3, 1/3, 1, & 3.
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