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# If x and y are integers, is xy + 1 divisible by 3? 1) when x

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Director
Joined: 20 Sep 2006
Posts: 632
If x and y are integers, is xy + 1 divisible by 3? 1) when x [#permalink]

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01 Aug 2008, 17:17
If x and y are integers, is xy + 1 divisible by 3?

1) when x is divided by 3, the remainder is 1.
2) when y is divided by 9, the remainder is 8.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-integers-is-xy-1-divisible-by-189789.html

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Current Student
Joined: 31 Aug 2007
Posts: 365
Re: If x and y are integers, is xy + 1 divisible by 3? 1) when x [#permalink]

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01 Aug 2008, 17:38
I'm getting C...need to know each of x and y.
Director
Joined: 20 Sep 2006
Posts: 632
Re: If x and y are integers, is xy + 1 divisible by 3? 1) when x [#permalink]

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01 Aug 2008, 18:44
are you trying with diff numbers?
VP
Joined: 17 Jun 2008
Posts: 1285
Re: If x and y are integers, is xy + 1 divisible by 3? 1) when x [#permalink]

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01 Aug 2008, 21:44
3
rao_1857 wrote:
If x and y are integers, is xy + 1 divisible by 3?

1) when x is divided by 3, the remainder is 1.
2) when y is divided by 9, the remainder is 8.

Lets consider the given condition : x and y are integers ,+ve or -ve or 0

Question : is xy + 1 divisible by 3?
consider (1) : say x=4 ,4y+1 when y=1 not div by 3 and when y=2 div by 3 => insufficient => eliminate A,D
consider (2) : say y=17 ,17x+1 , x=2 => not div by 3 ,when x=1 => div by 3 => isufficient => eliminate B

consider (1) and (2) :
say x=3m+1 and y=9n+8 where m and n are integers=> xy+1=(3m+1)(9n+8)+1 =27mn+9n+24m+8+1 =27mn+9n+24m+9 => this is div by 3 always hence is sufficient => C is answer and eliminate E
IMO C
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cheers
Its Now Or Never

Director
Joined: 20 Sep 2006
Posts: 632
Re: If x and y are integers, is xy + 1 divisible by 3? 1) when x [#permalink]

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02 Aug 2008, 11:31
1
spriya wrote:
rao_1857 wrote:
If x and y are integers, is xy + 1 divisible by 3?

1) when x is divided by 3, the remainder is 1.
2) when y is divided by 9, the remainder is 8.

Lets consider the given condition : x and y are integers ,+ve or -ve or 0

Question : is xy + 1 divisible by 3?
consider (1) : say x=4 ,4y+1 when y=1 not div by 3 and when y=2 div by 3 => insufficient => eliminate A,D
consider (2) : say y=17 ,17x+1 , x=2 => not div by 3 ,when x=1 => div by 3 => isufficient => eliminate B

consider (1) and (2) :
say x=3m+1 and y=9n+8 where m and n are integers=> xy+1=(3m+1)(9n+8)+1 =27mn+9n+24m+8+1 =27mn+9n+24m+9 => this is div by 3 always hence is sufficient => C is answer and eliminate E
IMO C

Thanks spriya
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Joined: 09 Sep 2013
Posts: 7264
Re: If x and y are integers, is xy + 1 divisible by 3? 1) when x [#permalink]

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06 Dec 2017, 00:38
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Re: If x and y are integers, is xy + 1 divisible by 3? 1) when x   [#permalink] 06 Dec 2017, 00:38
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