GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Oct 2019, 21:32 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

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.  What is the unit digit of A=2+2^2+2^3+...+2^10?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Retired Moderator V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1333
Location: Viet Nam
What is the unit digit of A=2+2^2+2^3+...+2^10?  [#permalink]

Show Tags

2
4 00:00

Difficulty:   35% (medium)

Question Stats: 67% (01:11) correct 33% (01:35) wrong based on 108 sessions

HideShow timer Statistics

What is the unit digit of $$A=2+2^2+2^3+...+2^{20}$$?

A. 0
B. 2
C. 4
D. 6
E. 8

_________________
Senior Manager  B
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
Re: What is the unit digit of A=2+2^2+2^3+...+2^10?  [#permalink]

Show Tags

1
3
$$A=2+2^2+2^3+...+2^{20}$$

Sum of GP = $$\frac{2*(2^{20} - 1)}{2 - 1} = 2*(2^{20} - 1)$$

$$20$$ is a multiple of $$4$$ ----> $$2^{20}$$ has units digit $$6$$

$$2*(6 - 1) = 2*5 = 10$$

Units digit is $$0$$

Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4753
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: What is the unit digit of A=2+2^2+2^3+...+2^10?  [#permalink]

Show Tags

3
1
nguyendinhtuong wrote:
What is the unit digit of $$A=2+2^2+2^3+...+2^{20}$$?

A. 0
B. 2
C. 4
D. 6
E. 8

$$2^1 = 2$$
$$2^2 = 4$$
$$2^3 = 8$$
$$2^4 = 6$$
______________
Total = 0

There will be 5 such sets as $$2^4$$ , $$2^8$$, $$2^{12}$$ , $$2^{16}$$ & $$2^{20}$$ ; units digit in each case will be 0

So, The sum of the units digit of the series will be 0...

Answer will be (A) 0

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager  S
Joined: 05 Dec 2016
Posts: 237
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29 Re: What is the unit digit of A=2+2^2+2^3+...+2^10?  [#permalink]

Show Tags

Fisrt, find the cyclicity of 2 = 4 (2;4;8;6)
Second, find number of cycles
Since last number of set contains 2^20, so we have 20 as greatest power. 20 is a multiple of 4, 20/4=5. So we have 5 full cycles.
Lastly, we just need to sum up all possible values of powers 2+4+8+6=20, thus 0 is the unit digit, answer A.
Solved in 36 sec.
Manager  S
Joined: 25 Mar 2013
Posts: 226
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
What is the unit digit of A=2+2^2+2^3+...+2^10?  [#permalink]

Show Tags

Units digit pattern of 2 : 2,4,8,6
A set of 4 x 5 = 2^20
Units digit of sum of 2 to 2^20 is always 0
A
_________________
I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you
Non-Human User Joined: 09 Sep 2013
Posts: 13081
Re: What is the unit digit of A=2+2^2+2^3+...+2^10?  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: What is the unit digit of A=2+2^2+2^3+...+2^10?   [#permalink] 06 Feb 2019, 19:41
Display posts from previous: Sort by

What is the unit digit of A=2+2^2+2^3+...+2^10?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

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