It is currently 30 Sep 2020, 21:00
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.

If x is a positive integer such that the units digit of x^3

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 13432
Followers: 292

Kudos [?]: 3418 [0], given: 12318

CAT Tests
If x is a positive integer such that the units digit of x^3 [#permalink] New post 09 Dec 2017, 16:17
Expert's post
00:00

Question Stats:

66% (00:55) correct 33% (00:48) wrong based on 39 sessions
If x is a positive integer such that the units digit of \(x^3\) is 3, what is the units digit of \(x^{15}\) ?

A. 1
B. 3
C. 5
D. 7
E. 9
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Manager
Manager
Joined: 25 Nov 2017
Posts: 51
Followers: 0

Kudos [?]: 48 [0], given: 5

Re: If x is a positive integer such that the units digit of x^3 [#permalink] New post 09 Dec 2017, 19:35
If x^3 has 3 as unit digit, it must be 7^3 since it equals 343.
The 7 has the following pattern
7 ^1 7
7^2 9
7^3 3
7^4 1
7^5 7 and so one
So 7^15 has a 3 as unit digits. Since I did it quickly, I am pretty sure that it is false. Any help ?
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 13432
Followers: 292

Kudos [?]: 3418 [0], given: 12318

CAT Tests
Re: If x is a positive integer such that the units digit of x^3 [#permalink] New post 11 Dec 2017, 02:36
Expert's post
Explenation

\(X^3\) for ending in 3 must be \(7^3= 343\)

Seeing a repeating pattern for 7 every four numbers 7 starts over again.

A cycle of 14 end in 9. So, the next number must be ending in 3.

B is the answer
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

1 KUDOS received
Manager
Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 94 [1] , given: 99

Re: If x is a positive integer such that the units digit of x^3 [#permalink] New post 10 May 2018, 10:38
1
This post received
KUDOS
How about we divide 15/3 as it goes completely in 15.. the 15 power will have its unit digit ending as 3.. hence the option is B.
1 KUDOS received
Intern
Intern
Joined: 26 Apr 2019
Posts: 1
Followers: 0

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

Re: If x is a positive integer such that the units digit of x^3 [#permalink] New post 26 Apr 2019, 14:15
1
This post received
KUDOS
First of all, we can find out that when we multiply the same unit digit, they are following the same law
eg. 23*23=529, 63*63=3969 the unit digit remain the same

When x3' unit digit is 3, and x15=x3*x3*x3*x3*x3
3*3=9, 3*3*3=27, 3*3*3*3=81, 3*3*3*3*3=243,
so the unit digit is 3
2 KUDOS received
Intern
Intern
Joined: 27 Apr 2019
Posts: 2
Followers: 0

Kudos [?]: 3 [2] , given: 0

Re: If x is a positive integer such that the units digit of x^3 [#permalink] New post 27 Apr 2019, 06:33
2
This post received
KUDOS
Given : Units digit of x^3 is 3
To find : Units digit of x^15

Steps to solve:
1. x^15 can be written as (x^3)^5
2. W.K.T, x^3 is 3
3. Now , simplifying step 1 we get, i.e. 3^5 = 243

observe, the units digit here is 3

Hence, the option is B.

P.S. To solve 3^5 quickly, wk.t, 3^2=9
so, 3^5 it boils down to (3^2) (3^2) 3 =9*9*3=81*3=243

Hope, this helps!
Intern
Intern
Joined: 21 May 2020
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 33

Re: If x is a positive integer such that the units digit of x^3 [#permalink] New post 17 Jun 2020, 16:07
curiouscat wrote:
Given : Units digit of x^3 is 3
To find : Units digit of x^15

Steps to solve:
1. x^15 can be written as (x^3)^5
2. W.K.T, x^3 is 3
3. Now , simplifying step 1 we get, i.e. 3^5 = 243

observe, the units digit here is 3

Hence, the option is B.

P.S. To solve 3^5 quickly, wk.t, 3^2=9
so, 3^5 it boils down to (3^2) (3^2) 3 =9*9*3=81*3=243

Hope, this helps!


I read it the same way as you and solved it the same way too. Thanks for re-assuring this method is the quickest!
Re: If x is a positive integer such that the units digit of x^3   [#permalink] 17 Jun 2020, 16:07
Display posts from previous: Sort by

If x is a positive integer such that the units digit of x^3

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.