Last visit was: 12 Jul 2025, 03:25 It is currently 12 Jul 2025, 03:25
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,636
Own Kudos:
740,612
 [9]
Given Kudos: 98,172
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,636
Kudos: 740,612
 [9]
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,681
Own Kudos:
19,431
 [6]
Given Kudos: 165
Expert
Expert reply
Posts: 3,681
Kudos: 19,431
 [6]
2
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
General Discussion
avatar
NeoNguyen1989
Joined: 18 Nov 2018
Last visit: 06 May 2025
Posts: 84
Own Kudos:
Given Kudos: 42
Posts: 84
Kudos: 87
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 12 July 2025
Posts: 8,346
Own Kudos:
4,813
 [2]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy)
GMAT Focus 1: 545 Q79 V79 DI73
Posts: 8,346
Kudos: 4,813
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
What is the remainder when \(3^0 + 3^1 + 3^2 + ... + 3^{2009}\) is divided by 8?

(A) 0
(B) 1
(C) 2
(D) 4
(E) 6

slightly different approach and method i used
cyclicity of 3 ;
3^0=1 , 3^1 = 3, 3^2 = 9; 3^3= 7 ; 3^4 = 1
so for set of every 4 no we get a repeat of unit digits
1+3+9+7 ; 20 now 2009 times would be 20*100= 2000+ 9 units more i.e two more cycles of 3 ; 20+20 and 1 of 3^1= 43
our last digits would be ~ 2000+43; 2043
when 2043 divided by 8 ; 255*8 ; 2040 ; ~ 3 remainder ; best answer is 4
IMO D
avatar
vgabrov
Joined: 12 Mar 2019
Last visit: 17 Dec 2022
Posts: 5
Given Kudos: 10
Posts: 5
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
NeoNguyen1989
call A = 3^0 + 3^1 + ... + 3^2009
3A = 3^1 + 3^2 + ... + 3^2010
3A - A = 3^2010 - 3^0
2A = 3^2010 - 1
A = (3^2010 - 1) / 2
A = [ (3^2)^1005 -1 ] / 2
A = [(8 + 1)^1005 - 1] / 2
A = [8^1004 + 8^1003 + ... + 8^1 + 1 -1] / 2
A = [8^1003 * 4 + 8^1002 * 4 + ... + 8*4 + 4]
A divides 8 and have remainder of 4. D is the answer

Are you sure the Newton's Binomial formula is correct here, and there shouldn't be a 8^1005 in it as well? (8+1)^1005 = (8+1)*(8+1)^1004 = 8*8^1004+...=8^1005.
Though it doesn't alter the logic of the solution to the original question.
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 12 Jul 2025
Posts: 5,698
Own Kudos:
5,212
 [1]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
GMAT 1: 690 Q50 V34
Posts: 5,698
Kudos: 5,212
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the remainder when \(3^0 + 3^1 + 3^2 + ... + 3^{2009}\) is divided by 8?

(A) 0
(B) 1
(C) 2
(D) 4
(E) 6

Asked: What is the remainder when \(3^0 + 3^1 + 3^2 + ... + 3^{2009}\) is divided by 8?

3^0 + 3^1 + 3^2 + ... + 3^{2009}mod8 = 1 + 3 + 9 + 27 + .... 3^2009mod8 = (1 + 3 + 1 + 3+ 1+ 3 + ......2010 terms)mod8
= 4*1005mod8 = 4*5mod8 = 20mod8 = 4

IMO D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,375
Own Kudos:
Posts: 37,375
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
102636 posts
PS Forum Moderator
688 posts