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

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rockrock
 Post subject: When positive integer x is divided by 11, the quotient is y
 Post Posted: Tue Jul 27, 2010 1:32 pm 
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Course Students


Posts: 38
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?

a) 0
b) 1
c) 2
d) 3
e) 4

How would you approach this problem by picking numbers?

Also does anyone know if there is a Thursdays with Ron session that deals with advanced number properties/divisibility & primes?
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loving.achin
 Post subject: Re: When positive integer x is divided by 11, the quotient is y
 Post Posted: Wed Jul 28, 2010 12:21 pm 
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Students


Posts: 7
Hi rockrock,
We are given : x = 11*y + 3 ---(1)
x = 19*(P) + 3 ---(2)
Where P is some number.

=> That x leaves a remainder of 3 when divided by 11
and
x leaves a remainder of 3 when divided by 19

=> (x-3) is a multiple of 11
and
(x-3) is a multiple of 19

=> (x-3) is a multiple of both 11 and 19.

=> Take any number which is both multiple of 11 and 19. Divide it by 11 to get the value of y (i.e. find y from equation (1) above).

Lets take 11*19*200 to be the number. So (x-3) is 11*19*200
=> from equation (1) .....
x-3 = 11*y
=> y = 19 * 200


Now divide y by 19 => No remainder => 'A' is the solution
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rockrock
 Post subject: Re: When positive integer x is divided by 11, the quotient is y
 Post Posted: Mon Aug 02, 2010 4:04 pm 
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Course Students


Posts: 38
Thanks great explanation! The only difference I would've made would be to just multiply 11*19 to get 209 as (x-3). then plug that into y/19 = 11 with no remainder.

Really appreciate it!
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mschwrtz
 Post subject: Re: When positive integer x is divided by 11, the quotient is y
 Post Posted: Thu Sep 02, 2010 4:52 pm 
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ManhattanGMAT Staff


Posts: 506
Very clever direct approach.
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