Last visit was: 24 Apr 2026, 18:56 It is currently 24 Apr 2026, 18:56
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
amathews
User avatar
Joined: 07 Dec 2016
Last visit: 10 Oct 2017
Posts: 30
Own Kudos:
695
 [23]
Given Kudos: 29
Products:
My Reviews
Posts: 30
Kudos: 695
 [23]
What is the remainder when 7^9 - 4 is divided by 7? 14 Apr 2017, 04:32
2
Kudos
Add Kudos
21
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

73% (00:55) correct 27% (01:04) wrong based on 380 sessions

History

Date
Time
Result
Not Attempted Yet
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,459
 [9]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,459
 [9]
What is the remainder when 7^9 - 4 is divided by 7? Updated on: 12 Jul 2021, 09:37
Originally posted by BrentGMATPrepNow on 14 Apr 2017, 06:27.
Last edited by BrentGMATPrepNow on 12 Jul 2021, 09:37, edited 1 time in total.
6
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
amathews
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5
Show more

KEY STRATEGY: If we take 7^9 - 4 and add zero to it, the value doesn't change.

We're going to add zero by subtracting 3 and adding 3 at the same time.
So, 7^9 - 4 = 7^9 - 4 - 3 + 3
= 7^9 - 7 + 3
= 7(7^8 - 1) + 3
= 7(some integer) + 3

As we can see, our initial number can be rewritten as 3 more than some multiple of 7.
So, if we divide that number by 7, the remainder will be 3

Answer: C

RELATED VIDEO
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,087
 [6]
Given Kudos: 105,873
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,818
Kudos: 811,087
 [6]
What is the remainder when 7^9 - 4 is divided by 7? 14 Apr 2017, 04:36
4
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
amathews
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5
Show more

7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.

Answer: C.
General Discussion
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,903
Own Kudos:
5,454
 [3]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,903
Kudos: 5,454
 [3]
What is the remainder when 7^9 - 4 is divided by 7? 14 Apr 2017, 07:00
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
amathews
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5
Show more

\(\frac{7^9 - 4}{7}\)

\(= Rem ( 0 - 4 )\)

So, We have remainder -4

Thus, the value of the remainder will be \(7 - 4 = 3\)

Answer, must be (C) 3
User avatar
Chemerical71
User avatar
Joined: 09 Jan 2016
Last visit: 01 Sep 2020
Posts: 76
Own Kudos:
485
Given Kudos: 61
GPA: 3.4
WE:General Management (Human Resources)
Posts: 76
Kudos: 485
What is the remainder when 7^9 - 4 is divided by 7? 14 Apr 2017, 08:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
amathews
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5

7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.

Answer: C.
Show more
Hello Bunnel.
When it is 7^8 -4 then what would be remainder. Thanks in advance.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,087
Given Kudos: 105,873
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,818
Kudos: 811,087
What is the remainder when 7^9 - 4 is divided by 7? 14 Apr 2017, 08:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Chemerical71
Bunuel
amathews
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5

7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.

Answer: C.
Hello Bunnel.
When it is 7^8 -4 then what would be remainder. Thanks in advance.
Show more

It seems that you did not understand the explanation. The remainder of 7^n - 4 divided by 7 where n is a positive integer is always 3.
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 24 Apr 2026
Posts: 5,986
Own Kudos:
5,859
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,986
Kudos: 5,859
What is the remainder when 7^9 - 4 is divided by 7? 15 Aug 2020, 09:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Asked: What is the remainder when 7^9 - 4 is divided by 7?

(7^9-4)mod7 = -4mod7 = 3mod7

IMO C
avatar
ankitabiswas
avatar
Joined: 12 Jan 2017
Last visit: 13 Nov 2024
Posts: 8
Own Kudos:
6
 [1]
Given Kudos: 50
Concentration: Technology, Strategy
WE:Information Technology (Computer Software)
Posts: 8
Kudos: 6
 [1]
What is the remainder when 7^9 - 4 is divided by 7? 22 Aug 2020, 09:56
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can anyone please explain it again in simple terms. I am still not able to understand it. May be i am missing something here.
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,680
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,286
Kudos: 2,680
What is the remainder when 7^9 - 4 is divided by 7? Updated on: 17 Sep 2024, 07:54
Originally posted by BrushMyQuant on 20 Oct 2022, 10:10.
Last edited by BrushMyQuant on 17 Sep 2024, 07:54, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We need to find What is the remainder when \(7^9\) - 4 is divided by 7

Remainder of \(7^9\) - 4 by 7 = Remainder of \(7^9\) by 7 + Remainder of -4 by 7 = 0 + -4 = -4

=> Remainder = -4 + 7 = 3

So, Answer will be C
Hope it helps!

Watch following video to MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,975
Own Kudos:
1,117
Posts: 38,975
Kudos: 1,117
What is the remainder when 7^9 - 4 is divided by 7? 21 Feb 2024, 03:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109818 posts
Krunaal
Tuck School Moderator
853 posts