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

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Manager
Joined: 12 Feb 2006
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When the positive integer x is divided by 11, the quotient [#permalink]

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15 Feb 2007, 04:28
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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 three. What is the remainder when y is divided by 19?

A. 0
B. 1
C. 2
D. 3
E. 4

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Director
Joined: 06 Feb 2006
Posts: 893

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15 Feb 2007, 04:33
I pick A.

x/11=y+3
x/19=q+3

x=11y+3
x=19q+3

Substract one equation from the other.

11y-19q=0
11y=19q

Clearly from this we can see that y must have a factor of 19.... so the remainder will be 0.

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Retired Moderator
Joined: 05 Jul 2006
Posts: 1748

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15 Feb 2007, 05:04
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 three. What is the remainder when y is divided by 19?

A. 0
B. 1
C. 2
D. 3
E. 4

x = 11y+3

x = 19k+3

19k+3 = 11y+3

19k/11 = y

thus y is muktiple of 19 and remainder = 0

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Manager
Joined: 10 Dec 2005
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15 Feb 2007, 05:09
bz9 wrote:
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 three. What is the remainder when y is divided by 19?

A. 0
B. 1
C. 2
D. 3
E. 4

Same approach as yezzz my answer is also A as I get remainder = 0 too.
_________________

"Live as if you were to die tomorrow. Learn as if you were to live forever." - Mahatma Gandhi

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Manager
Joined: 12 Feb 2006
Posts: 115

Kudos [?]: 80 [0], given: 0

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04 Mar 2007, 00:21
Thanks Everyone,

OA is A and the explanations makes perfect sense.

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Senior Manager
Joined: 29 Jan 2007
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04 Mar 2007, 10:33
yezz, simaq
I also got 0 as remainder..but dint see it as obvious as you did.

when you have 19K/11 = y <=> 19*(k/11) = y
How did you know k/11 is integer to say y is multiple of 19.

I am sure I am missing some basic concept perhaps. So wanted to learn it.

Kudos [?]: 70 [0], given: 0

04 Mar 2007, 10:33
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