If x and y are integers, is xy + 1 divisible by 3?

(1) When x is divided by 3, the remainder is 1 --> x=3n+1, if x=1, then 1*y+1 when y=1 not div by 3 and when y=2 div by 3 => insufficient

(2) When y is divided by 9, the remainder is 8 -->y=9m+8, if y=1, then x*1+1 when x=1 not div by 9 and when x=8 div by 9 => insufficient

(1) + (2) :

x=3n+1 and y=9m+8 where m and n are integers=> xy+1=(3n+1)(9m+8)+1 =27mn+9m+24n+8+1 =27mn+9m+24n+9 => this is div by 3 always hence is sufficient => C

Ans. C)

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