GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 01 Mar 2021, 09:14
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
If x is an integer greater than 1, what is the units digit of 6^x − 6^
4 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 72148
CAT Tests Top Member of the Month
If x is an integer greater than 1, what is the units digit of 6^x − 6^ [#permalink] New post  22 May 2018, 03:29
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

91% (00:42) correct 9% (00:53) wrong based on 65 sessions

Hide Show timer Statistics

If x is an integer greater than 1, what is the units digit of \(6^x − 6^{(x−1)}\)?

A. 0
B. 1
C. 3
D. 6
R. It cannot be determined.
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
V
u1983
Current Student
Joined: 24 Aug 2016
Posts: 787
GMAT 1: 540 Q49 V16
GMAT 2: 680 Q49 V33
GMAT ToolKit User Reviews Badge
If x is an integer greater than 1, what is the units digit of 6^x − 6^ [#permalink] New post  22 May 2018, 03:49
Bunuel wrote:
If x is an integer greater than 1, what is the units digit of \(6^x − 6^{(x−1)}\)?

A. 0
B. 1
C. 3
D. 6
R. It cannot be determined.


It does not matter how many times 6 is multiplied by 6. The unit's digit is always 6 (unless x is 0 or -ve).
Hence , Units digit of both \(6^x\) & \(6^{(x−1)}\) is \(6\).
Hence after subtraction the units digit is 0.
Hence , I would go for option A.
_________________
Please let me know if I am going in wrong direction.
Thanks in appreciation.
Signature Read More
User avatar
S
Tulkin987
Manager
Manager
Joined: 28 Nov 2017
Posts: 134
Location: Uzbekistan
If x is an integer greater than 1, what is the units digit of 6^x − 6^ [#permalink] New post  22 May 2018, 03:56
Bunuel wrote:
If x is an integer greater than 1, what is the units digit of \(6^x − 6^{(x−1)}\)?

A. 0
B. 1
C. 3
D. 6
R. It cannot be determined.


If \(x=1\), then the units digit of \(6^x − 6^{(x−1)}\) is \(6-1=5\)

For all other cases \(...6-...6 = ...0\)

Answer: A
_________________
Kindest Regards!
Tulkin.
Signature Read More
User avatar
V
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3664
Re: If x is an integer greater than 1, what is the units digit of 6^x − 6^ [#permalink] New post  22 May 2018, 04:15
Expert Reply

Solution



Given:
• The value of the integer x is greater than 1

To find:
• The unit digit of the expression \(6^x\) – \(6^{(x-1)}\)

Approach and Working:
• If we observe the unit digit pattern of 6, we can see for any positive power of 6, the number will always end with 6 only
    o \(6^1\) = 6
    o \(6^2\) = 36
    o \(6^3\) = 216 etc.
• As x > 1, x-1 > 0
    o Hence, \(6^x\) and \(6^{(x-1)}\) will always end with the unit digit 6
• Therefore, \(6^x\) - \(6^{(x-1)}\) will end with 0
Hence, the correct answer is option A.

Answer: A
_________________







Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Signature Read More
GMAT Club Bot
gmatclubot
[#permalink]
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
9506 posts
Bunuel
Math Expert
72148 posts
VeritasKarishma
Veritas Prep GMAT Instructor
11470 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2415 posts
generis
Senior SC Moderator
4550 posts
Feedback

cron

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

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions