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What is the remainder when the positive integer n is divided

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reply2spg
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What is the remainder when the positive integer n is divided [#permalink] New post   10 May 2009, 21:09
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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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Re: What is the remainder when the positive integer n is divided [#permalink] New post   11 May 2009, 21:38
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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.


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 [#permalink] New post   25 Feb 2011, 07:40
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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.
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   11 May 2009, 03:41
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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

D

P.S > I hope i'm not missing something
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   11 May 2009, 08:42
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I think its B.

From stat 1, n could be 6 or 11. Both numbers give different remainders when divided by 2.Insuff.

From stat 2, n can be 11, 21, 31, etc. In all cases, it gives a remainder of 1 when divided by 2. Suff.
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   11 May 2009, 09:12
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n is +ive int, rem when n/2?

1)n/5, rem is odd

test numbers 13,21,28

13/2 rem=1, 21/2 rem=1, 28/2 rem=0, insuff

2)n/10, rem is odd

test numbers 13, 21, 27

13/2 rem=1, 21/2 rem=1, 27/2 rem =1, suff

B
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   28 Sep 2009, 22:50
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1) n = 5q + odd

^This doesn't tell us whether q is divisible by 2 or not. So this info is insufficient.

2) n = 10q + odd,
= 2(5q) + odd

^We can see that the remainder is odd. So this info is sufficient. B
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   08 Jul 2014, 03:38
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?
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What is the remainder when the positive integer n is divided [#permalink] New post   08 Jul 2014, 04:34
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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.

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] New post   17 Jun 2019, 01:26
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.



when n=13 ; 13/5 remainder=3(odd no) ; 13/2 remainder =1
when n=14 ; 14/5 remainder =1 ( odd no); 14/2 remainder= 0
when n= 16 ; 16/5 remainder =1 (odd no); 16/2 remainder = 0
when n=18 ; 18/5 remainder=3 (odd no) ; 18/2 remainder =0
when n= 21 ; 21/5 remainder =1 (odd no) ; 21/2 reaminder= 1

in all no we are nt getting a definite value of n so how statement 2 is sufficient?
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   17 Jun 2019, 01:33
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SUNILAA 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.

Answer: B.

P. S. naaga please always tag your questions.



when n=13 ; 13/5 remainder=3(odd no) ; 13/2 remainder =1
when n=14 ; 14/5 remainder =1 ( odd no); 14/2 remainder= 0
when n= 16 ; 16/5 remainder =1 (odd no); 16/2 remainder = 0
when n=18 ; 18/5 remainder=3 (odd no) ; 18/2 remainder =0
when n= 21 ; 21/5 remainder =1 (odd no) ; 21/2 reaminder= 1

in all no we are nt getting a definite value of n so how statement 2 is sufficient?


14 divided by 5 gives the remainder of 4, not 1. Also, you are analyzing statement (1) there, which is not sufficient.

Statement (2) says: When n is divided by 10, the remainder is an odd integer
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   19 Sep 2023, 07:15
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Re: What is the remainder when the positive integer n is divided [#permalink]
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