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# What is the remainder when integer n is divided by two?

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Math Expert
Joined: 02 Sep 2009
Posts: 58318
What is the remainder when integer n is divided by two?  [#permalink]

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10 Jan 2017, 03:53
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Difficulty:

75% (hard)

Question Stats:

61% (02:04) correct 39% (01:58) wrong based on 92 sessions

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What is the remainder when integer n is divided by two?

(1) When n is divided by 3, the remainder is odd.
(2) When n is divided by 5, the remainder is odd.

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Re: What is the remainder when integer n is divided by two?  [#permalink]

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10 Jan 2017, 09:58
statement 1: number n= 3x+1

n can be 7 or 4 so insufficient

Statement 2: number is either 5x+1 or 5x+3

n can be 21 or 6 so insufficient

Combining both : n can be 16 or 13 so insufficient

Correct ans is E

+1 Kudos if you like the post
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Re: What is the remainder when integer n is divided by two?  [#permalink]

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10 Jan 2017, 10:48
Bunuel wrote:
What is the remainder when integer n is divided by two?

(1) When n is divided by 3, the remainder is odd.
(2) When n is divided by 5, the remainder is odd.

(1) n=3x+1
two cases
1st is when x is odd then 3x+1 =odd+odd=even
remainder=0
2nd is when x is even then 3x+1= even+odd = odd
remainder =1
Not suff...

(2) n=5x+1
two cases
1st is when x is odd then 5x+1 =odd+odd=even
remainder=0
2nd is when x is even then 5x+1= even+odd = odd
remainder =1
Not suff...

combining both n is multiple of both 3 &5 thus
n=15x+1

two cases
1st is when x is odd then 15x+1 =odd+odd=even
remainder=0
2nd is when x is even then 15x+1= even+odd = odd
remainder =1
Not suff...

Ans E
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Joined: 03 Sep 2018
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What is the remainder when integer n is divided by two?  [#permalink]

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15 Jan 2019, 02:55
Stem: $$n$$ $$mod$$ $$2$$

I) $$n=3k+(2p+1)$$ $$\implies$$ $$Remainder_n=0+1$$ OR $$Remainder_n=1+1$$ $$\implies$$ $$NS$$

II) $$n=5L+(2m+1)$$ $$\implies$$ $$Remainder_n=0+1$$ OR $$Remainder_n=1+1$$ $$\implies$$ $$NS$$

I&II) $$n=15x+5=5(3x+1)$$ Which is essentially the same issue as under I & II:
$$Remainder_n=1*1$$ OR $$Remainder_n=1*0$$ $$\implies$$ $$NS$$
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What is the remainder when integer n is divided by two?   [#permalink] 15 Jan 2019, 02:55
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