Divisibility and remainder

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lightbulb: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Wed Jul 09, 2008 6:40 pm; Thanked: 3 times

by lightbulb » Mon Nov 17, 2008 9:49 am

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

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Source: Beat The GMAT — Data Sufficiency | Mon Nov 17, 2008 9:49 am

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

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

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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lightbulb: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Wed Jul 09, 2008 6:40 pm; Thanked: 3 times

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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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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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lightbulb: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Wed Jul 09, 2008 6:40 pm; Thanked: 3 times

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

Like this post

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