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

Oldest

Best Reply

Author

Message

TAGS:

SVP

Joined: 18 Nov 2004

Posts: 1544

Followers: 2

Kudos [?]: 9 [0], given: 0

What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is [#permalink]

18 Mar 2005, 13:57

00:00

Question Stats:

0% (00:00) correct

0% (00:00) wrong

based on 0 sessions

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

Last edited by banerjeea_98 on 18 Mar 2005, 14:36, edited 1 time in total.

Manager

Joined: 11 Jan 2005

Posts: 58

Location: Mexico City

Followers: 1

Kudos [?]: 3 [0], given: 0

[#permalink]

18 Mar 2005, 14:29

i get 2

It took me a minute to get to 950 as the sum but after that it is easy.

Add the digits of 950 so 9+5+0=14 divide by = 2 with remainder 2.

Remainders when the sum of the digits is divided by 3 and 6 are the same as the actual number. so 452: 4+5+2= 11 divide 11 by 3 and get 3 with 2 remainder.

divide 452 get 150 with 2 remainder :smoke

Intern

Joined: 23 Jan 2005

Posts: 32

Location: Ft. Worth, TX

Followers: 0

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

[#permalink]

18 Mar 2005, 14:36

You don't need to add the numbers individually.

if you list them out individually:

91 92 93 94 95 96 97 98 99

you can see the average of these numbers is 95. since there are 10 numbers total, 95*10 = 950.

950 / 6 = 158, remainder 2.
_________________

thanks,
hornsfan2005

SVP

Joined: 18 Nov 2004

Posts: 1544

Followers: 2

Kudos [?]: 9 [0], given: 0

[#permalink]

18 Mar 2005, 14:37

guys try it again, I have updated the ques, there was an error before.

Senior Manager

Joined: 15 Mar 2005

Posts: 434

Location: Phoenix

Followers: 1

Kudos [?]: 7 [0], given: 0

Re: PS [#permalink]

18 Mar 2005, 15:25

banerjeea_98 wrote:

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

Let A = 9^9 + 9^8 + ... + 9^1

9A = 9^10 + (9^9 + 9^8 + ... + 9^2 + 9^1) - 9^1
9A = 9^10 + A - 9
8A = 9^10 - 9
A = (9^10 - 9)/8
= 9( 9^9 -1)/8

Since 9^9 = (9^3)^3

A = 9 ((9^3)^3 - 1)/8
= 9 (729^3 -1)/8

Since a^3 - b^3 = (a-b)^3 + 3ab(a-b)

A = 9/8[(729-1)^3 + 3*729(729-1)]
= 9/8[728^3 + 3*729*728]
= 9[91*728^2 + 3*729*91]

Dividing this by 6, we have this remainder
9[ 1*2*2 + 3*3*1 ] = 9*13 = 117 which leaves 3 as the remainder.

Thus I'd go with 3 as the answer.

Hope that helps.
_________________

Who says elephants can't dance?

SVP

Joined: 25 Nov 2004

Posts: 1582

Followers: 4

Kudos [?]: 13 [0], given: 0

Re: PS [#permalink]

18 Mar 2005, 22:41

banerjeea_98 wrote:

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

=9^1 + 9^2 + 9^3 + ...... + 9^9
sum of 1st term and 2nd term is even and when divided by 6 leaves 0 as reminder. similarly, sum of 3rd and 4th also result in even number which is divided by 6 and leaves 0 as reminders. so on for 5th and 6th, and 7th and 8th term. the only remaining term is 9th. the reminder is 3 no mater the value of 9^n.

Re: PS [#permalink] 18 Mar 2005, 22:41

	Similar topics	Author	Replies	Last post
Similar Topics:	What is the remainder when 9^1 + 9^2 + 9^3 +...+ 9^9 is	sunniboy007	5	13 Mar 2004, 16:32
	What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is	christoph	2	06 May 2005, 06:45
	What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is	cool_jonny009	15	12 Nov 2005, 01:09
	What is the reminder when 91 + 92 + 93 + ...... + 99 is	sm176811	11	05 Apr 2006, 02:11
	What is the reminder when 9^1 + 9^2 + 9^3 + ...... + 9^9 is	ashkrs	6	22 Dec 2007, 13:16

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

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

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

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

Main navigation

GMAT Resources

Partners

MBA Resources