My approach:
Stem: If x and y are integers, is xy + 1 divisible by 3?–> notice that xy+1 is divisible by three if xy is even (but not iff it is even)
(1) When x is divided by 3, the remainder is 1.x=3q+1
–> not divisible by 3
–> y could be divisible by 3 or it could not be, producing two different answers
–> Hence, NOT SUFFICIENT
(2) When y is divided by 9, the remainder is 8.–>Hence, the remainder when divided by 3 is also 8
–>However, x could be divisible by 3 or it could not be, producing two different answers
–>Hence, NOT SUFFICIENT
(1) & (2) together —>From 1, we know that remainder is 1
—>From 2, we know that remainder is 8
—>Iff the remainder product of xy and the sum of the remainder product of xy and 1 add to 3, xy+1 must be divisible
HENCE, (remainder x) * (remainder y) + (1) = 8*1+1= 9, hence, xy+1 is always divisible by 3:
C _________________
Good luck to you. Retired from this forum.