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

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VP
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When the positive integer x is divided by 11, the quotient [#permalink] New post 08 Aug 2006, 17:47
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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 3. What is the remainder when y is divided by 19?

A 0
B 1
C 2
D 3
E 4

please explain
VP
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Re: PS: Remainder [#permalink] New post 08 Aug 2006, 18:56
x = 11 (y) + 3 ..........i
x = 19 n + 3..............ii

11 (y) + 3 = 19 n + 3
11 (y) = 19 n

the only values that satisfies y and n are multiples of 19 and 11 respectively. if y is a multiple of 19, the reminder is 0 when y is divided by 19.

A.
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 [#permalink] New post 08 Aug 2006, 19:31
I tried to get the answer by picking numbers
I couldn't get one:(
VP
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 [#permalink] New post 08 Aug 2006, 20:59
A 0

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

As 11x19 = 209, x can be 209k + 3 where k is a +ve integer.

Therefore y =19.
VP
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 [#permalink] New post 08 Aug 2006, 21:08
haas_mba07 wrote:
y =19.


nope. y is a multiple of 19. it could be 0 or 19 or 38 or so on.
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 [#permalink] New post 08 Aug 2006, 22:31
A

x = 11y + 3
x/19 will have remainder only if y is divisible by 19.

Hence y/19 will yield zero remainder.
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

  [#permalink] 08 Aug 2006, 22:31
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