QB - NP: #5 Dividing by 11 & 19

[jeremy.hansen]

I don't understand the explanation to this question and I am hoping I can get perhaps a simpler one.

Question: 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?



I know that the first sentence can be translated into x = 11Y + 3 (or x -3 is a multiple of 11)

And that the second sentence means x = 19A + 3 (or x -3 is a multiple of 19)

What I am having trouble with is seeing that Y is a multiple of 19. It would be helpful is someone could show me with real numbers.

thanks
Jeremy

[gayathri248]

x = 11Y + 3
x = 19A + 3

so, 11Y = 19A. For this equation to be true, Y should have atleast one multiple of 19 as a factor since 11 doesn't divide 19.

[tim]

Nice, succinct explanation; good job..