The Official Guide For GMAT® Quantitative Review, 2ND Edition
If x and y are positive integers, what is the remainder when 10^x + y is divided by 3 ?
(1) x = 5
(2) y = 2
We can see that 10^x + y will always be of the form 10+y , or 100 +y or 1000+y etc depending on the power of x
so 1 is always going to be carried forward from the 10^x side to y
if x= 1 and y = 1 then 10^x+y will give 10+1 =11, divided by 3 remainder 2
if x= 2 and y = 1 then we have 100+1 =101,divided by 3 remainder 2
if x=2 and y =2 then we have 100+2 =102,divided by 3 remainder 0
hence the remainder really depends on the value of y
1) if y = 1 remainder is 2, if y is 2 remainder is 0, since no info about y hence insuff.
2)X=2 , just what we were looking for , no matter what ever is the value of x remainder will always be 0.
as 10^x+y will always be of the form:
etc remainder in all cases is 0 hence B is suff
answer is B