GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Oct 2019, 05:52

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

17^27 has a units digit of:

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 15 Sep 2018
Posts: 9
17^27 has a units digit of:  [#permalink]

Show Tags

New post Updated on: 16 Sep 2018, 00:58
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

82% (00:41) correct 18% (01:00) wrong based on 89 sessions

HideShow timer Statistics

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, 09:09.
Last edited by Bunuel on 16 Sep 2018, 00:58, edited 1 time in total.
Renamed the topic and edited the question.
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4771
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: 17^27 has a units digit of:  [#permalink]

Show Tags

New post 15 Sep 2018, 09:30
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)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Senior Manager
Senior Manager
User avatar
D
Joined: 18 Jun 2018
Posts: 262
Re: 17^27 has a units digit of:  [#permalink]

Show Tags

New post 15 Sep 2018, 09:33
1
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 \(3\).

please check below link for more info about cyclicity concept
https://gmatclub.com/forum/cyclicity-on ... 13019.html
Intern
Intern
avatar
B
Joined: 15 Sep 2018
Posts: 9
Re: 17^27 has a units digit of:  [#permalink]

Show Tags

New post 15 Sep 2018, 10:02
Great - Thank you both very much!
Intern
Intern
avatar
Joined: 20 Dec 2018
Posts: 45
Re: 17^27 has a units digit of:  [#permalink]

Show Tags

New post 21 Dec 2018, 21:39
We know that 7n can have unit digit of 7 , 9, 3 and 1.
We can find the unit digit by dividing n by 4. If the remainder is 1 then the unit digit will be 7, for remainder =2 unit digit = 9, for remainder = 3 unit digit = 3 for remainder = 0 unit digit = 1.
So, dividing 27 by 4 we get a remainder = 3.
Hence, the unit digit is 3.
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: 17^27 has a units digit of:  [#permalink]

Show Tags

New post 10 Jan 2019, 10:12
Aviv29 wrote:
17^27 has a units digit of:

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

\(? = \left\langle {{{17}^{27}}} \right\rangle = \left\langle {{7^{27}}} \right\rangle\)

\(\left\langle {{7^4}} \right\rangle = \left\langle {{7^2} \cdot {7^2}} \right\rangle = \left\langle {\left\langle {{7^2}} \right\rangle \cdot \left\langle {{7^2}} \right\rangle } \right\rangle = 1\)

\(\left\langle {{7^{24}}} \right\rangle = \left\langle {{7^4} \cdot {7^4} \cdot \ldots \cdot {7^4}} \right\rangle = {\left\langle {{7^4}} \right\rangle ^6} = 1\)

\(? = \left\langle {{7^{24}} \cdot {7^3}} \right\rangle = \left\langle {{7^{24}}} \right\rangle \cdot \left\langle {{7^3}} \right\rangle = 1 \cdot 3 = 3\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMAT Club Bot
Re: 17^27 has a units digit of:   [#permalink] 10 Jan 2019, 10:12
Display posts from previous: Sort by

17^27 has a units digit of:

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne