from the stem we know that "when the positive integer x is divided by 11, the quotient is y and the remainder 3" this can also be rewritten as:

x = 11*y+3

the same way that 30/7 = 4 and a remiander of 2

7*4+2 = 30

after we arrived to x = 11*y+3 we are told that x will also give a remiander of 3 when divided in 19, so:

x/19 = (11*y+3)/19 = will give a remainder of 3

we are asked what will be the remainder when y/19 , we don't know, but we can try to solve for (11*y+3)/19

one not so good way to solve is to plug numbers ! I don't like this way , but we will use it later on for check.

we are still stuck with (11*y+3)/19 , now if (11*y+3)/19 gives a remiander of 3 , we can say that 11*y/19 will give us a remainder of 0 ! (since we took out the 3, if we will add it the remainder will be once again 3)

but we were asked about y/19, not 11*y/19.

Since 19 is a prime number it will be very easy to find y that will give us 11*y/19 = an integer (no remiander).

y=19

11*19/19 = 11

so 19/19 will give you yet again a remiander of 0.

The answer is (A)