Suppose xy are positive integers such that xy = 2835. If the HCF of x and y is 9, then what are the possible values of 2x +y ?

Upon finding the prime factors of 2835, we get $$7\times\ 5\times\ 3^4$$
Since we know that the HCF of x and y is 9, the $$3^4$$ must be split equally between x and y. 
Now the possible pair values of x and y are (315, 9) or (45,63) {This we get by distributing the remaining 5 and 7 between x and y}
of these pairs, we cannot we cannot find the exact values of x and y. 
So we will have to find the possible combinations for 2x+y and find those values. 
x=9 and y=315 gives us 333
x=63 and y=45 gives us 171
x=45 and y=63 gives us 153
x=315 and y=9 gives us 639

We can see that of all of these values, 333 and 153 are in the option C. 
Hence, Option C is the correct answer.