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What is the tens digit of 6^17?

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Re: What is the tens digit of 6^17? [#permalink]

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New post 15 Sep 2017, 03:58
Raths wrote:
What is the tens digit of 6^17?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


Here is a post discussing the use of pattern recognition for last two digits:
https://www.veritasprep.com/blog/2014/1 ... ns-part-i/
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Re: What is the tens digit of 6^17? [#permalink]

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New post 15 Sep 2017, 07:55
Tens digit of 6^17. To start, the tens digit can also be calculated considering the same as (6^17/100). Taking out the common factors making the same equation as 6^2*((6^15)/100) so further simplifying the equation becomes 9*((6^15)/25). Now checking the divisibility cycle of 6^x/25 and finding the remainder tof 1. So the cycle is of 5 so the remainder when 15 is divided by 5 is 0 which is the last term of the cycle and the remainder is 1. So 9*1=9 and since we simplified by dividing by 4 so now multiplying the same by 4. So the answer becomes 4*9=36 and hence the tens place is 3 and the answer is B.

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Re: What is the tens digit of 6^17? [#permalink]

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New post 21 Sep 2017, 09:07
6^17 = (2×3)^17 = 2^17 × 3^17
Now, 2^17 = 2^10 × 2^7 = 24 × 28 = 72
And 3^17 = 3^16 × 3 = 81^4 ×3 = 21 × 3 = 63
Lasr two digit = 72 × 63 = 36
Tens digit = 3

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Re: What is the tens digit of 6^17?   [#permalink] 21 Sep 2017, 09:07

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What is the tens digit of 6^17?

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