The unit digit in the sum of $${\left( {124} \right)^{372}}\,$$  $$ + \,{\left( {124} \right)^{373}}$$  = ?

A. 5

B. 4

C. 2

D. 0

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & {\left( {124} \right)^{372}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\left( {124} \right)^{373}} \cr & \,\,\,\mathop {{4^{372}}}\limits^ \downarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathop {{4^{373}}}\limits^ \downarrow \cr} $$
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