If 2305 + 303 is divided by 9, then the remainder is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 2.
(a + b)2 = a2 + 2ab + b2 = am + b2
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a + b)n = am + bn
Remainder of (303/9) = 6
2305 = 22.2303 = 4.(23)101 = 4(9 - 1)101 = 4[9m + (-1)101] = 4(9m - 1) = 36m - 4 = 9p - 4
Remainder of (2305/9) = -4
Total remainder of [(2305 + 303)/9] = -4 + 6 = 2