Captchar wrote:When a positive integer is divided by 4, the remainder is r; when divided by 9, the remainder is R. What is the greatest possible value of r^2+R?

To maximize (r^2 + R), we need to maximize both r and R.

Now, maximum value of r, i.e. maximum value of the remainder when any number is divided 4 is 3.
And, maximum value of R, i.e. maximum value of the remainder when any number is divided 9 is 8.

Hence, the maximum value of (r^2 + R) is (3^2 + 8) = (9 + 8) = 17

The correct answer is C.

aman88 wrote:Sir, the possible remainders of 9 are all the integers from 1-8, right?
And similarly, possible remainders of 4 are 1,2,3, right?

Yes, that's correct.