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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
1
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]

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New post 26 Jan 2019, 20:09
Raths wrote:
What is the tens digit of 6^17?

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



Whats the problem source? It's pretty challenging and I cant think of a quick way to solve it. I also couldnt understand Bunuels explanation. Could someone help break this problem down into an easily digestible format?
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Re: What is the tens digit of 6^17?  [#permalink]

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New post 26 Jan 2019, 21:05
Raths wrote:
What is the tens digit of 6^17?

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


IF you are able to identify the pattern you should be good, I find this approach i fool proof one

6
36
216
1296
7776
46656
xxxx36

Now after that point you need not solve, as tens digit will be same after this, After every 5th term the series will start again

Remove the first term 6 from the series, you will be left with 16 terms, making, 3 as the correct answer

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Re: What is the tens digit of 6^17?   [#permalink] 26 Jan 2019, 21:05

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