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

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What is the remainder when the positive integer n is divided [#permalink]  25 Feb 2011, 06:20
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What is the remainder when the positive integer n is divided by 2?

(1) When n is divided by 5, the remainder is an odd integer.
(2) When n is divided by 10, the remainder is an odd integer
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Math Expert
Joined: 02 Sep 2009
Posts: 25207
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Kudos [?]: 25084 [1] , given: 2702

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Expert's post
naaga wrote:
What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 5, the remainder is an odd integer.
(2) When n is divided by 10, the remainder is an odd integer

What is the remainder when the positive integer n is divided by 2?

Question basically asks whether n is odd or even: if it's odd then the remainder will be 1 and if it's even then the remainder will be zero.

(1) When n is divided by 5, the remainder is an odd integer --> n=5q+odd, so n could be odd (1, 3, 11, 13, 21, 23, ...) as well as even (6, 8, 16, 18, ... ). Not sufficient.

(2) When n is divided by 10, the remainder is an odd integer --> n=10p+odd=even+odd=odd. Sufficient.

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Kudos [?]: 25 [0], given: 11

If divided by 10 ,and the remainder is odd, then remainder will always be 1 when divided by 2
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Kudos [?]: 191 [0], given: 123

Clear B. 2) tells me precisely that n is odd. Hence reminder is 1 when n is divided by 2.
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Kudos [?]: 20 [0], given: 5

1. in suff
no will be like 6,8,11,13

2. suff - no will be always odd-11,13 15 , 17

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Kudos [?]: 136 [0], given: 10

Clear B, as 10 is a multiple of 2.Since the remainder is an odd number meaning it is always 1.
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Director
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Kudos [?]: 82 [0], given: 42

1. Not sufficient

n could be even or odd

2. Sufficient
n is even +odd => n is odd

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Kudos [?]: 36 [0], given: 0

Re: What is the remainder when the positive integer n is divided [#permalink]  10 Oct 2013, 10:36
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Kudos [?]: 12 [0], given: 19

Re: What is the remainder when the positive integer n is divided [#permalink]  08 Jul 2014, 02:38
Bunuel wrote:
naaga wrote:
What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 5, the remainder is an odd integer.
(2) When n is divided by 10, the remainder is an odd integer

What is the remainder when the positive integer n is divided by 2?

Question basically asks whether n is odd or even: if it's odd then the remainder will be 1 and if it's even then the remainder will be zero.

(1) When n is divided by 5, the remainder is an odd integer --> n=5q+odd, so n could be odd (1, 3, 11, 13, 21, 23, ...) as well as even (6, 8, 16, 18, ... ). Not sufficient.

(2) When n is divided by 10, the remainder is an odd integer --> n=10p+odd=even+odd=odd. Sufficient.

Bunuel,

how can the remainder of n/5 be 11 or 6 and so on? Isn't it always between 1 and 4? e.g. 9/ 5 = 1+4 or 23 / 5 = 1+3.
What am I getting wrong here?
Math Expert
Joined: 02 Sep 2009
Posts: 25207
Followers: 3419

Kudos [?]: 25084 [0], given: 2702

What is the remainder when the positive integer n is divided [#permalink]  08 Jul 2014, 03:34
Expert's post
unceldolan wrote:
Bunuel wrote:
naaga wrote:
What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 5, the remainder is an odd integer.
(2) When n is divided by 10, the remainder is an odd integer

What is the remainder when the positive integer n is divided by 2?

Question basically asks whether n is odd or even: if it's odd then the remainder will be 1 and if it's even then the remainder will be zero.

(1) When n is divided by 5, the remainder is an odd integer --> n=5q+odd, so n could be odd (1, 3, 11, 13, 21, 23, ...) as well as even (6, 8, 16, 18, ... ). Not sufficient.

(2) When n is divided by 10, the remainder is an odd integer --> n=10p+odd=even+odd=odd. Sufficient.

Bunuel,

how can the remainder of n/5 be 11 or 6 and so on? Isn't it always between 1 and 4? e.g. 9/ 5 = 1+4 or 23 / 5 = 1+3.
What am I getting wrong here?

Those are possible values of n, not the possible values of the remainders upon division n by 5.
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What is the remainder when the positive integer n is divided   [#permalink] 08 Jul 2014, 03:34
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