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# 17^27 has a units digit of:

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Intern
Joined: 15 Sep 2018
Posts: 4
17^27 has a units digit of:  [#permalink]

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Updated on: 15 Sep 2018, 23:58
1
00:00

Difficulty:

15% (low)

Question Stats:

88% (00:28) correct 12% (00:35) wrong based on 25 sessions

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17^27 has a units digit of:

(a) 1
(b) 2
(c) 3
(d) 7
(e) 9

Originally posted by Aviv29 on 15 Sep 2018, 08:09.
Last edited by Bunuel on 15 Sep 2018, 23:58, edited 1 time in total.
Renamed the topic and edited the question.
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Status: QA & VA Forum Moderator
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Location: India
GPA: 3.5
Re: 17^27 has a units digit of:  [#permalink]

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15 Sep 2018, 08:30
Aviv29 wrote:
17^ 27 has a units digit of:

(a)1
(b)2
(c)3
(d)7
(e)9

Some can explain to me how to solve this question?
Thank you for the support

$$7^1 = 7$$
$$7^2 = 9$$
$$7^3 = 3$$
$$7^4 = 1$$

$$7^5 = 7$$
$$7^6 = 9$$

So, 7 has Cyclicity of 4

Now, $$17^{27} = 17^{4*6}*7^{3}$$

Since , $$7^4 = 1$$ thus $$7^{24} = 1$$ and $$7^3$$ = Units digit 3

Thus, $$17^{27}$$ will have units digit as 3, Answer must be (C)
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Thanks and Regards

Abhishek....

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Manager
Joined: 18 Jun 2018
Posts: 230
Re: 17^27 has a units digit of:  [#permalink]

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15 Sep 2018, 08:33
Aviv29 wrote:
17^ 27 has a units digit of:

(a)1
(b)2
(c)3
(d)7
(e)9

Some can explain to me how to solve this question?
Thank you for the support

OA:C
7 has the cyclicity of 4 (7,9,3,1).
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
and so on

$$17^{27}= 17^{6*4+3}$$

So the unit digit of $$17^{27}$$ would be $$3$$.

https://gmatclub.com/forum/cyclicity-on ... 13019.html
Intern
Joined: 15 Sep 2018
Posts: 4
Re: 17^27 has a units digit of:  [#permalink]

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15 Sep 2018, 09:02
Great - Thank you both very much!
Re: 17^27 has a units digit of: &nbs [#permalink] 15 Sep 2018, 09:02
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