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Number property question...help

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Number property question...help

by scoutkb » Sat Apr 07, 2007 2:05 pm
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

I am having a very difficult time with these remainder type questions. Any help would be appreciated. Please explain!

Highlight for OA: A
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by jayhawk2001 » Sat Apr 07, 2007 2:45 pm
x / 11 yields y as quotient and 3 as remainder. So,
x = 11y + 3

Similarly, x/19 yields (say) z as quotient and 3 as remainder. So,
x = 19z + 3

Equating to x, we get
11y + 3 = 19z + 3
11y = 19z

We know that y and z are integers (as they are quotients).

y = 19z/11
which implies that z has to be a multiple of 11

So, y/19 = z/11 and since z is a multiple of 11, it yields 0 remainder

Hence A
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