Nov 28 08:00 PM PST  09:00 PM PST Magoosh is excited to offer you a free GRE practice test with video answers and explanations. If you’re thinking about taking the GRE or want to see how effective your GRE test prep has been, pinpoint your strengths and weaknesses with this quiz! Dec 02 07:30 AM PST  08:30 AM PST This webinar will focus on evaluating reading comprehension questions on the GRE and GMAT. This 60 minute class will be a mix of "presentation" and Q&A where students can get specific questions answered. Dec 04 10:00 PM PST  11:00 PM PST Regardless of whether you choose to study with Greenlight Test Prep, I believe you'll benefit from my many free resources.
Author 
Message 
TAGS:


Director
Joined: 16 May 2014
Posts: 597
Followers: 116
Kudos [?]:
683
[0], given: 64

GRE Math Challengeunits digit of 57^n [#permalink]
29 May 2014, 08:22
Question Stats:
84% (00:24) correct
15% (00:26) wrong based on 13 sessions
Which of the following could be the units digit of \(57^n\) where n is a positive integer? Indicate all such digits. (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 (F) 5 (G) 6 (H) 7 (I) 8 (J) 9
_________________
My GRE Resources Free GRE resources  GRE Prep Club Quant Tests If you find this post helpful, please press the kudos button to let me know !




Intern
Joined: 18 Jun 2014
Posts: 39
Followers: 1
Kudos [?]:
30
[1]
, given: 15

Re: GRE Math Challenge [#permalink]
07 Aug 2014, 02:41
1
This post received KUDOS
(B) 1 (D) 3 (H) 7 (J) 9



Intern
Joined: 10 Jun 2018
Posts: 32
Followers: 0
Kudos [?]:
21
[0], given: 4

Re: GRE Math Challengeunits digit of 57^n [#permalink]
04 Sep 2018, 19:14
Can someone please answer the question. As per me,we should get the answer from multiple of 7 . In which, all of the options are answer.



Intern
Joined: 08 Oct 2018
Posts: 9
Followers: 1
Kudos [?]:
8
[2]
, given: 2

Re: GRE Math Challengeunits digit of 57^n [#permalink]
14 Oct 2018, 15:28
2
This post received KUDOS
Easiest to just take the units number 7 from 57 and then test exponents of this. 7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, 7^5 =16807.
Once you get to 7^5, you notice the pattern for the units, 7...9...3...1...7. So regardless of the value of the exponent, the result for the units will be one of those 4 values.
The answers are 7, 9, 3, 1.
(You can test this by raising 57^2 and getting the answer 2349, which has the same tens and units number as 7^2. The same is for 57^3 = 185193)



Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 12
Kudos [?]:
184
[0], given: 4

Re: GRE Math Challengeunits digit of 57^n [#permalink]
28 Oct 2018, 02:06
NixonDutt wrote: Can someone please answer the question. As per me,we should get the answer from multiple of 7 . In which, all of the options are answer. Hi power \(x^2\) means x multiplied two times x*xSo \(57^n\) means 57*57*57...n times Each digit has a cyclicity when multiplied x timesSo 7 has cyclicity which repeats after every 4th term 7^1=7..7^2=7*7=9....7^3=7*7*7=9*7=3...7^4=7*7*7*7=3*7=1 So cyclicity is 7,9,3,1,7.... Also it is multiple of odd, so all even are out.. 5 as units digit requires 5 as a multiple but here we have 7..
_________________
Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html




Re: GRE Math Challengeunits digit of 57^n
[#permalink]
28 Oct 2018, 02:06





