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

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When the positive integer x is divided by 11, the quotient [#permalink] New post 28 Aug 2008, 15:51
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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Re: mgmat [#permalink] New post 28 Aug 2008, 18:13
bigtreezl 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 3. What is the remainder when y is divided by 19?


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A. has to be 0.

since 11 and 19 both are primes and x = 11y+3 = 19k+3, 11y = 19k.

to have 11y = 19k, y must be 19 or its multiple and k has to be 11 and its multiple. for ex:

if y = 19, k = 11
if y = 38, k = 22

and so on. if so, y yeilds 0 reminder when y is divided by 19.
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Re: mgmat [#permalink] New post 28 Aug 2008, 18:24
i think 0.
cos , both 11 and 19 are prime nos..
so the no that when divided by both of them , which leaves a remainder 3 is the LCM of 11 and 19 = 209.
so 209+3 = 211 is the reqd no. x

211/11 = 19 + 3=remainder
and 211/19=11+3(remainder)
here, y=19
so 19/19=1 rem=0.
is it OK?
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Re: mgmat [#permalink] New post 28 Aug 2008, 19:32
bigtreezl 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 3. What is the remainder when y is divided by 19?


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x=11y+3
x=19k+3
x= 11*19m+3 =11y+3
11y= 19*11m
y=19m

zero is the answer
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Re: mgmat [#permalink] New post 29 Aug 2008, 21:27
x2suresh wrote:
bigtreezl 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 3. What is the remainder when y is divided by 19?


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x=11y+3
x=19k+3
x= 11*19m+3 =11y+3
11y= 19*11m
y=19m

zero is the answer


Suresh, can you please explain how you wrote the following:
x= 11*19m+3 =11y+3

Thanks.
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Re: mgmat [#permalink] New post 29 Aug 2008, 21:31
lkothari wrote:
x2suresh wrote:
bigtreezl 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 3. What is the remainder when y is divided by 19?


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x=11y+3
x=19k+3
x= 11*19m+3 =11y+3
11y= 19*11m
y=19m

zero is the answer


Suresh, can you please explain how you wrote the following:
x= 11*19m+3 =11y+3

Thanks.


x=11y+3
x=19k+3
--> 11y=19k here y and k are integers
so y must be multiple of 19
and k must be multipe of 11
11y= 11*19m = 19* 11*n
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Re: mgmat   [#permalink] 29 Aug 2008, 21:31
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