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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]  15 Feb 2007, 03:28
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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
Director
Joined: 05 Feb 2006
Posts: 899
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Kudos [?]: 54 [0], given: 0

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.
SVP
Joined: 05 Jul 2006
Posts: 1516
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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

x = 11y+3

x = 19k+3

19k+3 = 11y+3

19k/11 = y

thus y is muktiple of 19 and remainder = 0
Manager
Joined: 10 Dec 2005
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Re: Number Properties DS [#permalink]  15 Feb 2007, 04:09
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.
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Manager
Joined: 12 Feb 2006
Posts: 115
Followers: 1

Kudos [?]: 29 [0], given: 0

Thanks Everyone,

OA is A and the explanations makes perfect sense.
Senior Manager
Joined: 29 Jan 2007
Posts: 450
Location: Earth
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Kudos [?]: 45 [0], given: 0

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.
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