The digit in unit's place of the product (2153)167 is -
A. 1
B. 3
C. 7
D. 9
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\left( {2153} \right)^{167}} \cr & {\text{unit digit = }}{{\text{3}}^{167}} \cr & {\text{unit digit }} \cr & {{\text{3}}^1} \to {\text{3}} \to {\text{3}} \cr & {{\text{3}}^2} \to 9 \to 9 \cr & {{\text{3}}^3} \to 27 \to 7 \cr & {{\text{3}}^4} \to 81 \to 1 \cr} $$This cycle will continue
⇒ divide the power of 3 by 4
$$\eqalign{ & \frac{{167}}{4} \Rightarrow {\text{remainder is 3}} \cr & {{\text{3}}^3} \Rightarrow 7 \cr & {\text{unit digit = }}1 \times 7 = {\text{ }}7 \cr} $$
Join The Discussion
Comments ( 1 )
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
(264)102+(264)103