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# When the positive integer x is divided by 11, the quotient

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Director
Joined: 10 Feb 2006
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When the positive integer x is divided by 11, the quotient [#permalink]

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30 Oct 2007, 20:27
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

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Current Student
Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12
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30 Oct 2007, 20:43
i get 0...

we know that x=11k+3 where 11K=y

11k+3=19N+3

we know that x=11*19(K+M)+3

y=209

209/19 remainder 0
SVP
Joined: 29 Aug 2007
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30 Oct 2007, 22:29
When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

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agree with above.

it has to be zero. x is a multiple of (11x19) plus 3. so y is a multiple of 19. so reminder is 0 if y is divided by 19.
Director
Joined: 10 Feb 2006
Posts: 657
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Kudos [?]: 322 [0], given: 0

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31 Oct 2007, 08:41
Ok, i'm still kinda confused.

we know that x = 11y+3 & x = q19 + 3

11y+ 3 = q19 + 3

y = q19/11 ---

so when y /19 = q19/11 / 19/1 ..... have i totally go overboard with this one.

???
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