parkhydel wrote:
If x is a positive integer, r is the remainder when x is divided by 4, and R is the remainder when x is divided by 9, what is the greatest possible value of r^2 + R ?
A. 25
B. 21
C. 17
D. 13
E. 11
PS18180.02
Lets assume x to be a few different numbers - 1,2,3,4,5,6,7,8,9 (Considering many numbers just to clarify the concept)
When x is divided by 4
1/4 - The remainder will be 1
2/4 - The remainder will be 2
3/4 - The remainder will be 34/4 - The remainder will be 0 (4 is directly divisible by 4)
5/4 - The remainder will be 1
6/4 - The remainder will be 2
7/4 - The remainder will be 38/4 - The remainder will be 0 (8 is directly divisible by 4)
9/4 - The remainder will be 1
If we notice, the cycle keeps on repeating and we learn that the highest remainder is 3 when x si divided by 4
Similarly when X is divided by 9
1/9 - The remainder will be 1
2/9 - The remainder will be 2
.....
The highest remainder can be
8/9 - Where the remainder can be 8 After which the remainder cycle will again start from 0
Now, to answer the question asked
r has a maximum remainder of 3 and R has a maximum remainder of 8
So r^2 + R = 3^2 + 8 = 17