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# What is the remainder when the positive integer n is divided

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VP
Joined: 22 Nov 2007
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What is the remainder when the positive integer n is divided [#permalink]  26 Jan 2008, 08:04
What is the remainder when the positive integer n is divided by 3?
(1) The remainder when n is divided by 2 is 1.
(2) The remainder when n + 1 is divided by 3 is 2.
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Kudos [?]: 2142 [0], given: 359

Re: remainder [#permalink]  26 Jan 2008, 09:17
Expert's post
B

1. 3 and 5 satisfy condition but have different remainders. Insufficient.

2. n+1=3k+2 ==> n=3k+1. remainder=1. sufficient.
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VP
Joined: 22 Nov 2007
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Kudos [?]: 193 [0], given: 0

Re: remainder [#permalink]  27 Jan 2008, 03:01
walker wrote:
B

1. 3 and 5 satisfy condition but have different remainders. Insufficient.

2. n+1=3k+2 ==> n=3k+1. remainder=1. sufficient.

can we solve this one with mod. arithmetic?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Kudos [?]: 2142 [0], given: 359

Re: remainder [#permalink]  27 Jan 2008, 06:45
Expert's post
(n+1)mod3=2

(n)mod3+1mod3=2

(n)mod3=2-1=1

it is too easy.
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Manager
Joined: 01 Jan 2008
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Schools: Booth, Stern, Haas
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Kudos [?]: 48 [0], given: 2

Re: remainder [#permalink]  27 Jan 2008, 07:39
walker wrote:
(n+1)mod3=2

(n)mod3+1mod3=2

(n)mod3=2-1=1

it is too easy.

what does word "mod" mean ?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 2142 [0], given: 359

Re: remainder [#permalink]  27 Jan 2008, 07:42
Expert's post
kazakhb wrote:
what does word "mod" mean ?

(n)(mod m) means remainder when n is divided by m
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CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Followers: 407

Kudos [?]: 2142 [0], given: 359

Re: remainder [#permalink]  30 Jan 2008, 02:03
Expert's post
Sorry, guys. My definition of mod was incorrect.

x=r(mod y) means x=k*y+r
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Re: remainder   [#permalink] 30 Jan 2008, 02:03
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