The unit digit in the sum of ( 124 )^372\, + \, ( 124 )^373 = ?

Answer: Option D

$$\begin{array}{rl}& {\left(124\right)}^{372}{\left(124\right)}^{373}\\ & \stackrel{\downarrow }{4^{372}}\stackrel{\downarrow }{4^{373}}\end{array}$$
When 4 has odd power then unit digit is 4, when 4 has even power then unit digit is 6

41	→	4	→	4
42	→	16	→	6
43	→	64	→	4
44	→	256	→	6
4372				4373
↓				↓
6		+		4	= 10 = 0

Last (unit) digit = 0