The remainder when 6666..∞ is divided by 10 is :
A. 3
B. 6
C. 5
D. 0
E. Cannot determined
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Since}}, \cr & \frac{6}{{10}} \to \,{\text{remainder}}\,{\text{is}}\,{\text{6}}{\text{}} \cr & \frac{{{6^6}}}{{10}} \to \,{\text{remainder}}\,{\text{is}}\,{\text{6}}{\text{}} \cr & \frac{{{6^{{6^6}}}}}{{10}} \to \,{\text{remainder}}\,{\text{is}}\,{\text{6}}{\text{}} \cr & \frac{{{6^{{6^{{6^6}}}}}}}{{10}} \to \,{\text{remainder}}\,{\text{is}}\,{\text{6}}{\text{}} \cr & \frac{{{6^{{6^{{6^{{6^6}}}}}}}}}{{10}} \to \,{\text{remainder}}\,{\text{is}}\,{\text{6}}\,{\text{and}}\,{\text{so}}\,{\text{on}}. \cr & \cr & {\text{Thus,}}\,{\text{in}}\,{\text{all}}\,{\text{the}}\,{\text{such}}\,{\text{cases}}\, \cr & {\text{The}}\,{\text{remainder}}\,{\text{will}}\,{\text{always}}\,{\text{be}}\,6 \cr} $$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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