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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]

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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]

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11 May 2009, 21:38
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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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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.

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

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

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25 Feb 2011, 07:20
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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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Re: What is the remainder when the positive integer n is divided [#permalink]

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05 Oct 2011, 12:53
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Ans is B

As per statement one the number can be either odd or even. but when u divide by 10 you will get odd integer only when you divide a odd integer

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

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11 May 2009, 03:41
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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.

(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]

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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]

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11 May 2009, 09:12
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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25 Feb 2011, 11:15

If divided by 10 ,and the remainder is odd, then remainder will always be 1 when divided by 2
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25 Feb 2011, 11:23
Clear B. 2) tells me precisely that n is odd. Hence reminder is 1 when n is divided by 2.
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30 Apr 2011, 18:35

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

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10 Oct 2013, 11:36
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Re: What is the remainder when the positive integer n is divided [#permalink]

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08 Jul 2014, 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.

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]

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08 Jul 2014, 04:34
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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Re: What is the remainder when the positive integer n is divided [#permalink]

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16 Dec 2014, 12:13
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Re: What is the remainder when the positive integer n is divided [#permalink]

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30 Jan 2016, 12:54
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Re: What is the remainder when the positive integer n is divided [#permalink]

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02 Feb 2016, 19:01
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.
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Re: What is the remainder when the positive integer n is divided [#permalink]

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20 Feb 2017, 23:48
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Re: What is the remainder when the positive integer n is divided [#permalink]

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21 Feb 2017, 16:05
St 1 Insuff, becuase if we divide 10/5 --> remainder 0 but 8/5 = 3

St2 Suff - All-odd /10 will give odd Int as remainder (Suff)

Re: What is the remainder when the positive integer n is divided   [#permalink] 21 Feb 2017, 16:05

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