When positive integer N is divided by 4, the remainder is 3. : PS Archive
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When positive integer N is divided by 4, the remainder is 3.

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CEO
Joined: 21 Jan 2007
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When positive integer N is divided by 4, the remainder is 3. [#permalink]

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08 Nov 2007, 07:14
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When positive integer N is divided by 4, the remainder is 3. Which of the following CAN BE a remainder of n/12?

2
40
82
10
11
Director
Joined: 13 Dec 2006
Posts: 518
Location: Indonesia
Followers: 6

Kudos [?]: 208 [0], given: 0

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08 Nov 2007, 07:17
11 is the answer.... say n is 23, then 23/4 will have remainder 3 and 23/12 will have remainder 11.

Amardeep
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Joined: 01 Nov 2007
Posts: 69
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Kudos [?]: 8 [0], given: 0

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08 Nov 2007, 09:18
It is 11

the remainder of n/12 has to be less than 12 and odd

we have only one option = 11
SVP
Joined: 05 Jul 2006
Posts: 1743
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Kudos [?]: 317 [0], given: 49

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09 Nov 2007, 10:11
When positive integer N is divided by 4, the remainder is 3. Which of the following CAN BE a remainder of n/12?

2
40
82
10
11

n = 4x+3

n = 12y+b

4x+3 = 12y+b

4x+3-12y = b ie: even+odd-even = odd

b is odd .............11 is the answer
Intern
Joined: 02 Dec 2007
Posts: 11
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Kudos [?]: 1 [0], given: 0

Re: PS Remainder - EVEN vs ODD [#permalink]

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02 Dec 2007, 07:17
The number is 4N + 3

so 4N + 3/12
N = 1 then remainder 7
N= 2 then remainder 11
N = 3 then remainder 3
N= 4 remainder 7
N= 5 remainder 11.
So the possible list of remianders are 3,7,11.
So the ans is E.
SVP
Joined: 21 Jul 2006
Posts: 1538
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Kudos [?]: 743 [0], given: 1

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02 Dec 2007, 10:38
wow, interesting to see each person with a completely different approach to reach to the same answer. that's really cool.
SVP
Joined: 28 Dec 2005
Posts: 1575
Followers: 3

Kudos [?]: 147 [0], given: 2

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15 Dec 2007, 10:58
Got E

given the stem, N must be an odd number.

Looking at n/12, the only way to get an odd number for n is to have an odd number as a remainder, because 12k always gives you an even number, and even + odd = odd
15 Dec 2007, 10:58
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