GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 01 Jun 2020, 09:06

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

Find the remainder when 25^18 is divided by 9

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

Hide Tags

Find Similar Topics 
SVP
SVP
avatar
V
Joined: 20 Jul 2017
Posts: 1506
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Find the remainder when 25^18 is divided by 9  [#permalink]

Show Tags

New post 02 Apr 2020, 04:06
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (01:47) correct 38% (01:39) wrong based on 60 sessions

HideShow timer Statistics

Find the remainder when \(25^{18}\) is divided by 9.

A. 1
B. 2
C. 3
D. 5
E. 6
GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4029
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Find the remainder when 25^18 is divided by 9  [#permalink]

Show Tags

New post 02 Apr 2020, 04:13
Dillesh4096 wrote:
Find the remainder when \(25^{18}\) is divided by 9.

A. 1
B. 2
C. 3
D. 5
E. 6


\(R[\frac{25^{18}}{9}] = R[\frac{(27-2)^{18}}{9}] = R[\frac{(-2)^{18}}{9}] = R[\frac{(2)^{18}}{9}] \)

\(R[\frac{(2)^{3}}{9}] = 8 or -1\) (negative remainder)

CONCEPT: Remainder can be written in both +ve and -ve form for simplification. When divisor is 9 and remainder is 7 then the number has either 7 in excess or number is 2 short to be divisible by 9 hence
Remainder (+7) = Remainder (-2) when divisor is 9


Taking exponent 6 both sides

\(R[\frac{(2)^{18}}{9}] = (-1)^6 = 1 \)

Answer: Option A

The concept video of remainder theorem is as follows:


_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes l Classroom Coaching l On-demand Quant course
Click Here for Uneditable GOOGLE reviews
Check website for most affordable Quant on-Demand course 2000+ Qns (with Video explanations)
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
Senior Manager
Senior Manager
User avatar
G
Status: Today a Reader; Tomorrow a Leader.
Joined: 14 Oct 2019
Posts: 406
Location: India
GPA: 4
WE: Engineering (Energy and Utilities)
Re: Find the remainder when 25^18 is divided by 9  [#permalink]

Show Tags

New post 02 Apr 2020, 06:14
METHOD I : Euler no of 9 = 9(1-1/3) = 6
rem [(25^18) /9]
= rem [(25^0)/9] [ 18 is divisible by 6 ]
= rem [1/9]
= 1

METHOD II : rem [(25^18 )/9]
=rem [ (-2)^18 /9] [ rem (25/9) = -2 ]
=rem [ (+2)^18 /9]
=rem [ (2^6) * ( 2^6 )* (2^6 )/9]
=rem [ 64*64*64 /9]
=rem [1*1*1 /9]
=1

METHOD III : rem [(25^18 )/9]
= rem [ (27-2)^18/9] [ using binomial theorem ]
=rem [ (-2)^18 /9] [ considering only last term since rest all terms will be divisible by 9 ]
=rem [ (+2)^18 /9]
=rem [ (2^6) * ( 2^6 )* (2^6 )/9]
=rem [ 64*64*64 /9]
=rem [1*1*1 /9]
=1

correct answer is A
Manager
Manager
avatar
G
Joined: 12 Mar 2019
Posts: 138
Re: Find the remainder when 25^18 is divided by 9  [#permalink]

Show Tags

New post 27 May 2020, 02:50
preetamsaha wrote:
METHOD I : Euler no of 9 = 9(1-1/3) = 6
rem [(25^18) /9]
= rem [(25^0)/9] [ 18 is divisible by 6 ]
= rem [1/9]
= 1

METHOD II : rem [(25^18 )/9]
=rem [ (-2)^18 /9] [ rem (25/9) = -2 ]
=rem [ (+2)^18 /9]
=rem [ (2^6) * ( 2^6 )* (2^6 )/9]
=rem [ 64*64*64 /9]
=rem [1*1*1 /9]
=1

METHOD III : rem [(25^18 )/9]
= rem [ (27-2)^18/9] [ using binomial theorem ]
=rem [ (-2)^18 /9] [ considering only last term since rest all terms will be divisible by 9 ]
=rem [ (+2)^18 /9]
=rem [ (2^6) * ( 2^6 )* (2^6 )/9]
=rem [ 64*64*64 /9]
=rem [1*1*1 /9]
=1

correct answer is A


hi, can you tell about euler theorem, What i know is
E(z)=z∗[1–1/P]∗[1–1/Q], where P and Q are prime factors of denominator
do we need 1 factor or 2 prime factors. In case we don't have 2 prime factors, Is 1 prime factor ok
GMAT Club Bot
Re: Find the remainder when 25^18 is divided by 9   [#permalink] 27 May 2020, 02:50

Find the remainder when 25^18 is divided by 9

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





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