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# What is the tens digit of 6^17?

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8891
Location: Pune, India
Re: What is the tens digit of 6^17?  [#permalink]

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15 Sep 2017, 02:58
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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Karishma
Veritas Prep GMAT Instructor

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Joined: 19 Sep 2016
Posts: 35
Re: What is the tens digit of 6^17?  [#permalink]

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15 Sep 2017, 06:55
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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Intern
Joined: 21 Sep 2017
Posts: 1
Re: What is the tens digit of 6^17?  [#permalink]

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21 Sep 2017, 08:07
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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Intern
Joined: 09 Mar 2017
Posts: 12
Re: What is the tens digit of 6^17?  [#permalink]

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26 Jan 2019, 19:09
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?
VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: What is the tens digit of 6^17?  [#permalink]

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26 Jan 2019, 20:05
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

B
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Re: What is the tens digit of 6^17?   [#permalink] 26 Jan 2019, 20:05

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