Divisibility and remainder

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Re: Divisibility and remainder

by logitech » Mon Nov 17, 2008 9:57 am
lightbulb wrote:If N is a positive integer and R is the remainder when (N-1)(N+1) is divided by 24, what is the value of R?

(1) N is not divisible by 2
(2) N is not divisible by 3

OA: C
1 2 3 4 5 6 7 8 9 10 11 12

1) 1, 3, 5, 7, 9, 11 ; (N-1)(N+1) is divided by 24 gives us different R

2) 1,2,4,5,7,8,10 ; (N-1)(N+1) is divided by 24 gives us different R

1+2 ) 1,5,7,11 ' (N-1)(N+1) is divided by 24 gives us 0 as the remainder

Hence, C
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Re: Divisibility and remainder

by lightbulb » Mon Nov 17, 2008 4:04 pm
Thanks for your response, but how do you generlize the case for numbers that are not mulitples of 2 or 3?
logitech wrote:
lightbulb wrote:If N is a positive integer and R is the
remainder when (N-1)(N+1) is divided by 24, what is the value of R?

(1) N is not divisible by 2
(2) N is not divisible by 3

OA: C
1 2 3 4 5 6 7 8 9 10 11 12

1) 1, 3, 5, 7, 9, 11 ; (N-1)(N+1) is divided by 24 gives us different R

2) 1,2,4,5,7,8,10 ; (N-1)(N+1) is divided by 24 gives us different R

1+2 ) 1,5,7,11 ' (N-1)(N+1) is divided by 24 gives us 0 as the remainder

Hence, C

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by cramya » Mon Nov 17, 2008 4:10 pm
Logitech's solution is good.

Refer to Ian's explanation also (as best as it can get)

https://www.beatthegmat.com/gmat-prep-re ... 16996.html

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by lightbulb » Mon Nov 17, 2008 4:36 pm
Nice one, thanks.
cramya wrote:Logitech's solution is good.

Refer to Ian's explanation also (as best as it can get)

https://www.beatthegmat.com/gmat-prep-re ... 16996.html