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?
A. 23
B. 21
C. 17
D. 13
E. 11
A. 23
B. 21
C. 17
D. 13
E. 11
To maximize (r^2 + R), we need to maximize both r and R.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?
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.
