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# n is a positive integer. What is the remainder when n is

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n is a positive integer. What is the remainder when n is [#permalink]

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09 Apr 2007, 11:59
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n is a positive integer. What is the remainder when n is divided by 6?

(1) n is a multiple of 3.
(2) When n is divided by 2, the remainder is 1.
[Reveal] Spoiler: OA
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09 Apr 2007, 12:20
n is +ve.

1. n = 3,6,9,12,15,...
insuff.

2. n = 3,5,7,9,11,13,15,..
insuff

together, n = 3,9,15,....
still insuff because of 3.

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09 Apr 2007, 12:38
if not E, then C
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09 Apr 2007, 15:40
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(C) for me

From 1
n could be 3, 6, 9, 12...

So:
o If n is odd, the reminder is 3 once divided by 6.
o If n is even, the reminder is 0 once divided by 6.

INSUFF.

From 2
When n is divided by 2, the remainer is 1. It's a definition on an odd integer.

n = 2*k + 1.

o If n = 7 then n/6 = 6*1 + 1
o If n = 9 then n/6 = 6*1 + 3

INSUFF.

1 & 2
Bingo ! This time, from 1 we know that we have to know if n is odd or even to be able to conclude. The stat 2 gives it to us.

SUFF.

Last edited by Fig on 09 Apr 2007, 23:43, edited 1 time in total.
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09 Apr 2007, 16:19
andrehaui wrote:
7. n is a positive integer. What is the remainder when n is divided by 6?

(1) n is a multiple of 3.
(2) When n is divided by 2, the remainder is 1.

solve and explain

From Stat1:
n= 6,9,12,15,18,21,24...
NS
From Stat2:
n is an odd integer
NS

From 1 & 2; n=9,15,21,24...
->remainder is 3

Both stat 1and2 are necessary->C!
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14 Apr 2007, 04:59
andrehaui wrote:
7. n is a positive integer. What is the remainder when n is divided by 6?

(1) n is a multiple of 3.
(2) When n is divided by 2, the remainder is 1.

solve and explain

n is a positive integer it can be even or odd. i.e it can be 1,2,3,4,5,6,7,8,...infinity. any number

now lets see what statement 1 has to say. statement 1 means the n is a multiple of 3 that is it can be 3,6,9,12,15,...,upto infinity i.e n=3a where a = 1,2,3,4,5,..infinity. when a is even then n is divisible by 6 and the remainder is 0 .but when a is odd n is divisible by 3 as it is multiple of 3 but not by 2 that is it is not divisible by 6 and we get a remainder equal to 1. so (1) is not sufficient.

similarly(2) is not sufficient. because in 2 we just know that n is a multiple of 2.

When we take (1)&(2) together. then statement 1 says that n is multiple of 3 and statement 3 says that n is multiple of 2 so can say that n is multiple of both 2 & 3 i.e 6. so n is completely divisible by 6. So the answere is (C).

Javed.

Cheers!
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14 Apr 2007, 06:21
Knowing that 1. n is a mutiple of 3 and 2. that it is odd tells us that everytime n is divided by 6, the remainder will be 3.

That is, for any number that is multiple of 3 and odd,
9,15,21, 27... r = 3, Therefore, C
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Re: n is a positive integer. What is the remainder when n is [#permalink]

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16 Mar 2014, 04:49
1. n = 3k --> n = 0,3,6,9,12,15....

if n = 3 R(n/6) = 3
if n = 6 R(n/6) = 0
if n = 9 R(n/6) = 3
if n = 12 R(n/6) = 0
.
.
.
NS ( Two possible remainders)

2. n = 2m + 1 --> n=1,3,5,7,9,...

if n = 1 R(n/6) = 1
if n = 3 R(n/6) = 3
if n = 5 R(n/6) = 5
if n = 7 R(n/6) = 1
if n = 9 R(n/6) = 3
.
.
.
NS ( Three possible remainders)

(1+2). n = 3, 9, 15,.... For every one of these numbers: R(n/6) = 3 ,SUFF.

C
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Re: n is a positive integer. What is the remainder when n is [#permalink]

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29 Jul 2016, 07:40
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Re: n is a positive integer. What is the remainder when n is   [#permalink] 29 Jul 2016, 07:40
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