Unit digit of the number (22)23 is :
A. 4
B. 6
C. 7
D. 8
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\left( {22} \right)^{23}} \cr & {\text{ Result unit digit}} \cr & {2^1}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,2\, \leftarrow | \cr & {2^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,\,\,\,\,\,\,\,\,\,|\,\,{\text{Cycle}} \cr & {2^3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,\,\,\,\,\,\,|\,\,\,{\text{Completes}} \cr & {2^4}\,\,\,\,\,\,\,\,\,\,\,\,\,\,16\,\,\,\,\,\,\,\,\,\,\,\,6 \leftarrow \,| \cr & {2^5}\,\,\,\,\,\,\,\,\,\,\,\,\,32\,\,\,\,\,\,\,\,\,\,\,\,2\,\,\, \cr & {\text{So divided power of 22 by 4 }} \cr & \frac{{23}}{4} = {\text{ remainder 3}} \cr & {2^3}\,\,\,\, = \,\,\,\,\,8\, \cr & {\text{unit digit = 8}} \cr} $$Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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