It is currently 13 Dec 2018, 02:31
My Tests

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.

GRE Math Challenge-units digit of 57^n

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 16 May 2014
Posts: 594
GRE 1: Q165 V161
Followers: 92

Kudos [?]: 439 [0], given: 64

GRE Math Challenge-units digit of 57^n [#permalink] New post 29 May 2014, 08:22
Expert's post
00:00

Question Stats:

75% (00:25) correct 25% (00:26) wrong based on 8 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

[Reveal] Spoiler: OA
B,D,H,J
[Reveal] Spoiler: OA

_________________

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 ! :)

1 KUDOS received
Intern
Intern
Joined: 18 Jun 2014
Posts: 42
Followers: 1

Kudos [?]: 26 [1] , given: 15

Re: GRE Math Challenge [#permalink] New post 07 Aug 2014, 02:41
1
This post received
KUDOS
(B) 1
(D) 3
(H) 7
(J) 9
Intern
Intern
Joined: 10 Jun 2018
Posts: 32
Followers: 0

Kudos [?]: 14 [0], given: 4

Re: GRE Math Challenge-units digit of 57^n [#permalink] New post 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.
1 KUDOS received
Intern
Intern
Joined: 08 Oct 2018
Posts: 9
Followers: 0

Kudos [?]: 5 [1] , given: 2

Re: GRE Math Challenge-units digit of 57^n [#permalink] New post 14 Oct 2018, 15:28
1
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: 203
Followers: 3

Kudos [?]: 63 [0], given: 1

CAT Tests
Re: GRE Math Challenge-units digit of 57^n [#permalink] New post 28 Oct 2018, 02:06
Expert's post
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*x
So \(57^n\) means 57*57*57...n times

Each digit has a cyclicity when multiplied x times
So 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/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: GRE Math Challenge-units digit of 57^n   [#permalink] 28 Oct 2018, 02:06
Display posts from previous: Sort by

GRE Math Challenge-units digit of 57^n

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.