BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

PS question- Beat the GMAT

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 48
Joined: Mon Oct 12, 2009 5:15 amFollowed by: 1 member
Thanked: 5 times
by lavinia » Thu Oct 21, 2010 6:43 am
What is the units digit of (18)to the power of 47 ?
A.0
B.2
C.4
D.6
E.8

Because we are asked for units digit of (18) to the power of 47, we should pay attention to (8) to the power of 7, right? But to simplify this, we can rewrite as [(2) to the power of 3] to the power of 7, which means (2) to the power of 21, and because we are looking for the units digit we should look at (2) to the power of 1, which equals 2. The correct answer is B.

Beat the GMAT video explanation is very good, but I feel this one is more easier. Could you please confirm that this approach is correct?

Thanks!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Community Manager
Posts: 991
Joined: Thu Sep 23, 2010 6:19 amFollowed by: 24 members
Location: Bangalore, India
Thanked: 146 times

by shovan85 » Thu Oct 21, 2010 7:13 am
lavinia wrote:What is the units digit of (18)to the power of 47 ?
A.0
B.2
C.4
D.6
E.8

Because we are asked for units digit of (18) to the power of 47, we should pay attention to (8) to the power of 7, right? But to simplify this, we can rewrite as [(2) to the power of 3] to the power of 7, which means (2) to the power of 21, and because we are looking for the units digit we should look at (2) to the power of 1, which equals 2. The correct answer is B.

Beat the GMAT video explanation is very good, but I feel this one is more easier. Could you please confirm that this approach is correct?

Thanks!
How about using cyclicity .

8^1 = 8 --> Unit digit 8
8^2 = 64 --> Unit digit 4
8^3 = 512 --> Unit digit 2
8^4 = 4096 --> Unit digit 6
8^5 = 32768 --> Unit digit 8

So the unit digit sequence repeats as 8,4,2,6,8,4,.....

Each 4 consecutive terms' unit digit repeat, Hence the cyclicity = 4.

Now 18^47
If u divide 47 by 4 we will get a remainder 3

And we know 8^3 unit digit is 2 from the cyclicity table.
If the problem is Easy Respect it, if the problem is tough Attack it
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members
Location: Milpitas, CA
Thanked: 447 times

by Rahul@gurome » Thu Oct 21, 2010 8:17 pm
There is one more approach.
(18)^47 = (3^47)*(6^47).
Now 6 raised to a power which is a positive integer always ends in 6.
So 6^47 ends in 6.
Next consider 3^47.
3^1 ends in 3.
3^2 ends in 9.
3^3 ends in 7.
3^4 ends in 1.
47 = 4*11 + 3.
So 3^47 ends in the same last digit in which 3^3 ends which is 7.
Taking into account that 6^47 ends in 6 and 3^47 ends in 7 and since 7*6 = 42 ends in 2, we conclude that (3^47)*(6^47) = 18^47 ends in 2.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1