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number properties

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Manager
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Joined: 04 Sep 2006
Posts: 113

Kudos [?]: 62 [0], given: 0

number properties [#permalink]

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New post 29 Jan 2009, 10:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

q: if n is a +ve integer , what is the remainder when n+1 * n-1 is divided by 24?

1. n is not divisible by 3
2. n is not divisible by 2

pls explain

Kudos [?]: 62 [0], given: 0

Manager
Manager
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Joined: 05 Jul 2008
Posts: 136

Kudos [?]: 123 [0], given: 40

GMAT 2: 740 Q51 V38
Re: number properties [#permalink]

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New post 29 Jan 2009, 10:30
vcbabu wrote:
q: if n is a +ve integer , what is the remainder when n+1 * n-1 is divided by 24?

1. n is not divisible by 3
2. n is not divisible by 2

pls explain

A, B is wrong

n is not divisible by 3 so n = 3k+1 or n= 3k+2. In both cases, (n+1)(n-1) is divisible by 3.
n is not divisible by 2 so n+1 and n-1 are both even. They are two consecutive even numbers so one of them is divisible by 4. So (n+1)(n-1) is divisible by 8

(n+1)(n-1) is divisible by 8 and by 3 => it is divisible by 24
C

Kudos [?]: 123 [0], given: 40

Senior Manager
Senior Manager
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Joined: 30 Nov 2008
Posts: 485

Kudos [?]: 360 [0], given: 15

Schools: Fuqua
Re: number properties [#permalink]

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New post 29 Jan 2009, 13:48
DavidArchuleta wrote:
vcbabu wrote:
q: if n is a +ve integer , what is the remainder when n+1 * n-1 is divided by 24?

1. n is not divisible by 3
2. n is not divisible by 2

pls explain

A, B is wrong

n is not divisible by 3 so n = 3k+1 or n= 3k+2. In both cases, (n+1)(n-1) is divisible by 3.
n is not divisible by 2 so n+1 and n-1 are both even. They are two consecutive even numbers so one of them is divisible by 4. So (n+1)(n-1) is divisible by 8

(n+1)(n-1) is divisible by 8 and by 3 => it is divisible by 24
C


Agree with C. I was trying to solve it by picking the numbers.

But this is a better solution.

Kudos [?]: 360 [0], given: 15

Re: number properties   [#permalink] 29 Jan 2009, 13:48
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