Latest apptitude Aptitude Question SOLUTION: When 31^31^301 divided by 9 what is the remainder?

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(#M40154126) APPTITUDE Numerical Ability question logic Keep an EYE

When 31^31^301 divided by 9 what is the remainder?

Asked In apptitude sree uma (9 years ago)

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Sanjoy Debnath  (9 years ago)

[31^31^301] % 9 .............. here % operator stands for reminder after divide
= [(3*9 +4)^31^301] % 9
= [4^31^301] %9

Now, 4^3 = 64 = 9*7 + 1
hence we first should find reminder of 31^301 when divided by 3

[31^301] % 3
= [(3*10 + 1) ^ 301] % 3
= [1^301] % 3
= 1
therefor we can conclude
[31^301] = 3*integer + 1 = 3i+1 (say)


hence
[31^31^301] % 9
= [4^31^301] %9
= [4^(3i+1)] % 9
= [4*(4^3i)] % 9
=[4*(64^i)]%9
=[4*{9*7 + 1}^i] % 9
= [4*{1}^i] % 9
=[4] % 9
= 4

hence reminder = 4

enjoy

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