The average of three consecutive odd numbers is 52 more than $${\frac{1}{3}^{{\text{rd}}}}$$ of the largest of these numbers. What is the smallest of these numbers?

A. 79

B. 75

C. 81

D. 77

Answer: Option D

Solution(By Examveda Team)

Let the three consecutive odd numbers are
$$\eqalign{ & x,\,x + 2,\,x + 4 \cr & \frac{{x + x + 2 + x + 4}}{3} = \frac{1}{3}\left( {x + 4} \right) + 52 \cr & \frac{{3x + 6}}{3} = \frac{{x + 4 + 156}}{3} \cr & 3x + 6 = x + 4 + 156 \cr & 2x = 154 \cr & x = 77 \cr} $$