If (67⁶⁷ + 67) is divided by 68, the remainder is :

A. 1

B. 63

C. 66

D. 67

Answer: Option C

Solution(By Examveda Team)

(xⁿ + aⁿ) is divisible by (x + a) when n is odd
∴ (67⁶⁷ + 1⁶⁷) is divisible by (67 + 1)
⇒ (67⁶⁷ + 1) is divisible by 68
⇒ On dividing (67⁶⁷ + 67) by 68, we get (67 - 1) = 66 as remainder.