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Hi there,

Could you explain in the simplest this concept and how to resolve it

If n is a positive integer, what is the hundreds' digit of 30(exponent (n)) ?

(1) 30(exponent (n)) > 1000
(2) n is the multiple of 3.

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rahulmehra13: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Wed Jul 22, 2009 8:49 am; Thanked: 4 times

Re:

by rahulmehra13 » Wed Aug 26, 2009 11:07 am

1)
30^n > 1,000
=> n >=3 (since 30^1=30, 30^2=900, 30^3=27000 > 1000)

So 30^n will always have minimum 3 zeros
=> Hundreds digit is 0.
Sufficient.

2)
Same as above since n=3k
30^3k = (27000) ^k.
So minimum 3 zeros
=> Hundreds digit is 0.
Sufficient.

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