Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Aug 2015, 13:12
GMAT Club 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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Director
Director
User avatar
Joined: 08 Jun 2007
Posts: 584
Followers: 2

Kudos [?]: 81 [0], given: 0

What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is [#permalink] New post 22 Dec 2007, 12:16
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is divided by 6?

(1) 0
(2) 3
(3) 4
(4) 2
(5) None of these
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 432

Kudos [?]: 2341 [0], given: 359

GMAT ToolKit User Premium Member
 [#permalink] New post 22 Dec 2007, 13:39
Expert's post
B

9^1(mod 6)=3
9^2(mod 6)=3
9^3(mod 6)=3
...
9^n(mod 6)=3

or

9^n=6m+r
3*3*9^(n-1)=3*2m+r ==> r should be divisible by 3 and be odd ==> r=3

we have 9*3=27 ==> 27(mod 6) =3
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 884
Followers: 6

Kudos [?]: 334 [0], given: 33

GMAT ToolKit User
Re: PS - Remainder Question. [#permalink] New post 22 Dec 2007, 18:11
ashkrs wrote:
What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is divided by 6?

(1) 0
(2) 3
(3) 4
(4) 2
(5) None of these



I think remainder should be 1, which is None of These.

So choice 5th.

9^1/6 , gives r=1

and the pattern continues giving remainder 1.

What is the OA?
SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2493
Followers: 61

Kudos [?]: 593 [0], given: 19

Re: PS - Remainder Question. [#permalink] New post 22 Dec 2007, 19:18
ashkrs wrote:
What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is divided by 6?

(1) 0
(2) 3
(3) 4
(4) 2
(5) None of these


1. 9/6 = 3 reminder
2. 9^2/6 = (6+3)^2 /6 = (6^2 + 2.6.3 + 3^2)^2 /6 = 3 reminder cuz (6^2) and (2.6.3) has 0 reminder and (3^2) has 3 reminder.
3. 9^3/6 = (6+3)^3 /6 = (6^3 + 3.6^2.3 + 3.6.3^2 + 3^3) /6 = 3 reminder

similarly 9^n has 3 reminder.
so if we add nine 3 reminders, the sum is 9x3 = 27, which alio has 3 reminder.

so B.
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 884
Followers: 6

Kudos [?]: 334 [0], given: 33

GMAT ToolKit User
Re: PS - Remainder Question. [#permalink] New post 22 Dec 2007, 19:21
GMAT TIGER wrote:
ashkrs wrote:
What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is divided by 6?

(1) 0
(2) 3
(3) 4
(4) 2
(5) None of these


1. 9/6 = 3 reminder
2. 9^2/6 = (6+3)^2 /6 = (6^2 + 2.6.3 + 3^2)^2 /6 = 3 reminder cuz (6^2) and (2.6.3) has 0 reminder and (3^2) has 3 reminder.
3. 9^3/6 = (6+3)^3 /6 = (6^3 + 3.6^2.3 + 3.6.3^2 + 3^3) /6 = 3 reminder

similarly 9^n has 3 reminder.
so if we add nine 3 reminders, the sum is 9x3 = 27, which alio has 3 reminder.

so B.



The mistake I was doing was, I simplified 9/6 = 3/2 ( which will have the remainder as 1)

But why can't we simplify the terms?
SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2493
Followers: 61

Kudos [?]: 593 [0], given: 19

Re: PS - Remainder Question. [#permalink] New post 22 Dec 2007, 22:34
LM wrote:
GMAT TIGER wrote:
ashkrs wrote:
What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is divided by 6?

(1) 0
(2) 3
(3) 4
(4) 2
(5) None of these


1. 9/6 = 3 reminder
2. 9^2/6 = (6+3)^2 /6 = (6^2 + 2.6.3 + 3^2)^2 /6 = 3 reminder cuz (6^2) and (2.6.3) has 0 reminder and (3^2) has 3 reminder.
3. 9^3/6 = (6+3)^3 /6 = (6^3 + 3.6^2.3 + 3.6.3^2 + 3^3) /6 = 3 reminder

similarly 9^n has 3 reminder.
so if we add nine 3 reminders, the sum is 9x3 = 27, which alio has 3 reminder.

so B.



The mistake I was doing was, I simplified 9/6 = 3/2 ( which will have the remainder as 1)

But why can't we simplify the terms?


9/6 = 3/2, but they have different reminders and in case of reminder question its wrong to to do so.

also 9/6= 18/12 but again they have different reminders. so this is the trick...
CEO
CEO
User avatar
Joined: 29 Mar 2007
Posts: 2585
Followers: 17

Kudos [?]: 259 [0], given: 0

Re: PS - Remainder Question. [#permalink] New post 23 Dec 2007, 20:45
ashkrs wrote:
What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is divided by 6?

(1) 0
(2) 3
(3) 4
(4) 2
(5) None of these


not sure if there is a quicker way, but I usually solve these by establishing a pattern.

9/6--> R=3
9+81/6--> R=0

9+81+729/6 --> 819/6 R=3 so every odd it will have a R of 3.

B.
Re: PS - Remainder Question.   [#permalink] 23 Dec 2007, 20:45
Display posts from previous: Sort by

What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.