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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.

Without testing numbers:

First, there are only two remainders possible when you divide n by 2: 0 and 1. The remainder is 0 if n is even, and 1 if n is odd. So the question is really just asking "is n odd?"

Remember the quotient/remainder definition. When we divide n by d, we have n = qd + r, where r is the remainder and q the quotient.

From S1, n = 5q + r, where r is odd. So n = 5q + odd, and n could be even if q is odd, and n could be odd if q is even. Insufficient.

From S2, n = 10q + r where r is odd. So n = even + odd = odd. Sufficient.
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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

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.

Answer: B.

P. S. naaga please always tag your questions. _________________

Re: What is the remainder when the positive integer n is divided [#permalink]

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11 May 2009, 02:41

1

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reply2spg 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.

(1) Let n = 8, remainder 3.....so, 8/2 = remainder = 0 Let n = 16, remainder 1....so 16/2 = remainder = 0 Suff (2) n = can be 10,30,50,70,90,110,130 etc All these numbers are divisible by 2, remainder = 0 Suff

Re: What is the remainder when the positive integer n is divided [#permalink]

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10 Oct 2013, 10:36

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Re: What is the remainder when the positive integer n is divided [#permalink]

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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.

Answer: B.

P. S. naaga please always tag your questions.

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?

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.

Answer: B.

P. S. naaga please always tag your questions.

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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Re: What is the remainder when the positive integer n is divided [#permalink]

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16 Dec 2014, 11:13

Hello from the GMAT Club BumpBot!

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Re: What is the remainder when the positive integer n is divided [#permalink]

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30 Jan 2016, 11:54

Hello from the GMAT Club BumpBot!

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Re: What is the remainder when the positive integer n is divided [#permalink]

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02 Feb 2016, 18:01

1. n can be 3, then the reminder will be 1, or n can be 8, and the remainder is 0. NS 2. n is odd, thus, the remainder when n is divided by 2 will always be 1.

gmatclubot

Re: What is the remainder when the positive integer n is divided
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02 Feb 2016, 18:01

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