Working on the equation:

x = 551 - 51y

y must be such that 51y is 51 + a multiple of 5 so it is y = 1 + 5k

For k = 1 the solution is (49,6), thus the sum is 55.

Is OA = c
Well the answer is 55

55*6 = 306 and the remaining 245/5 = 49

So X+Y = 49+5 = 55

To write this in terms of x we get
x = (551 - 51y)/5

For x to be an integer.. 551-51y needs to be a multiple of 5.. for that to happen it should either end with a 0 or a 5..

For ending with a 0 51*y should yield a number ending with 1.. we already know that 1 satisfies it.. the next number would be 11.. but that gives a number greater than 551.. so can't take that..

So now we should check another number that when subtracted from 551 should yield a number ending with 5.. so that means, 51y should be a number ending with 6..
the closest we have is itself.. and so that gives us y =6 and x = 49

total = 55.

Notice that the next number after 6 would be 16 and that too will give a number greater than 551, so not allowed..

how long do top scorers take on these kinds of questions? are these the questions considered "hard" or does it get way harder than that? i found the solution by working my way up from 1 until i reached 6.... but i guess to score high one needs to do it a smart way like you guys :-/