Symbiosis National Aptitude Test SNAP 2017 Paper

the common remainder be x. Then numbers (34041 - x) and (32506 - x) would be completely divisible by n.
Hence the difference of the numbers (34041 - x) and (32506 - x) will also be divisible by n or (34041 - x - 32506 + x) = 1535 will also be divisible by n.
Now, using options we find that 1535 is divisible by 307.