If N has remainder 6 when divided by 205, N is 6 more than a multiple of 205.
Since the question has to work with ANY SUCH N, we can just choose '211.' 211 has remainder 1 when divided by 5, so the answer must be B.
More abstractly, anything that is 6 more than a multiple of 205 is 6 more than a multiple of 5. But anything that is 6 more than a multiple of 5 is also **1 more** than the *next* multiple of 5 (for instance, 61 is 6 more than multiple of five 55, but also 1 more than multiple of five 60). Multiples of 5 *come in fives*, and the remainders cycle from 0, 1, 2, 3, 4, 0, 1, 2, 3, 4 etc...
So the remainder will be 1.
Some takeaways:
--Anytime a question asks, "If [x], then what is the answer to the question?" No matter HOW VAGUE 'x' seems, it must be enough to answer (unless there's the rare "not enough to answer the question" answer). So pick ANY SITUATION that fits 'x,' and you'll be able to answer (that strategy is very useful for this tricky question:
https://gmatclub.com/forum/if-xy-1-what ... 07238.html)
--If a number has remainder 'r' when divided by 'x,' it is *r more than a multiple of x*.
--When dividing by integer 'x,' remainders will cycle from 0 to (x-1), where remainders of 0 are multiples of x. No matter what the remainder is, the next number that has the same remainder when dividing by x can be found by adding x.
--If a number is r more than a multiple of x, it is also *r more than all the factors of x* (in this question, for instance, N is 6 more than a multiple of 205, so it's also 6 more than a multiple of 5 (and therefore 1 more than the next multiple of 5), and 6 more than a multiple of 41, which means N also has remainder 6 when divided by 41).