Statement 1 tells us that y is a two digit prime number. We know that x > y. If y = 11 and x = 22, the remainder would be 0. Alternatively, y could be 11 and x could be 21 and the remainder 10.buoyant wrote:If x and y are both positive integers and x>y , what is the remainder when x is divided by y ?
(1) y is a two-digit prime number.
(2) x= qy+9 , for some positive integer q
[spoiler]OA: C[/spoiler]
Insufficient
One might be tempted to say that Statement 2 is sufficient because it tells us that x = (a multiple of y) + 9. So one's initial inclination might be to jump and say the remainder is 9. The problem is that y might be equal to or smaller than 9, in which cases the remainder would be some number less than 9.
Insufficient
Together we know that x = (a multiple of y) + 9 and, since y is a two digit number, that y is greater than 9. So the remainder is 9.
Sufficient
Choose C.
