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30 Mar 2021, 05:00
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D
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Difficulty:
5%
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Question Stats:
87% (00:45) correct
13%
(01:04)
wrong
based on 111
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30 Mar 2021, 05:22
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Bunuel
Cyclicity is the concept in which the unit digit repeats in a cyclic manner
The cyclicity of the Unit digit of any number with unit digit 7 is 4.
i.e. Unit digit of a number with unit digit 7 repeats after every 4th power
e.g. \(7^1 = 7\)
\(7^2 = 49\)
\(7^3 = 343\)
\(7^4 = 2401\)
\(7^5 = 7\) at unit's place
SImilarly, cyclicity of unit digit of any number with units digit 6 is 1.
i.e. the unit digit remains same for any higher power of number which has units place 6
i.e. unit’s digit of \(16^4 * 27^3\) = unit’s digit of \(6^4 * 7^3\) = unit’s digit of \(6*3 = 8\)
Answer: Option D
30 Mar 2021, 05:28
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IMO D
Cyclinicity for 16 = 6
Cyclinicity for 7 = 3
Unit's digit = 8
Cyclinicity for 16 = 6
Cyclinicity for 7 = 3
Unit's digit = 8
