Last visit was: 25 Apr 2026, 04:10 It is currently 25 Apr 2026, 04:10
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,141
 [18]
Given Kudos: 105,878
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: 109,822
Kudos: 811,141
 [18]
GMAT Club Around The World!!! What is the remainder when 3^50 is 31 Dec 2021, 11:15
Kudos
Add Kudos
18
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
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:

74% (01:11) correct 26% (01:51) wrong based on 421 sessions

History

Date
Time
Result
Not Attempted Yet
What is the remainder when \(3^{50}\) is divided by 7?

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

 


This Month's Questions are Sponsored by
Experts' Global for the GMAT Club SC Butler

 

Experts Global

 





Happy New Year Nepal

Dec 31 Event: GMAT Club Around The World!
(38 new questions posted every hour time zone on Dec 31!)

ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,141
 [3]
Given Kudos: 105,878
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: 109,822
Kudos: 811,141
 [3]
GMAT Club Around The World!!! What is the remainder when 3^50 is 02 Jan 2022, 15:00
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
What is the remainder when \(3^{50}\) is divided by 7?

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




Happy New Year Nepal

Dec 31 Event: GMAT Club Around The World!
(38 new questions posted every hour time zone on Dec 31!)

Show more

Experts' Global Video Official Explanation

General Discussion
User avatar
ElninoEffect
User avatar
Joined: 07 Apr 2020
Last visit: 06 Mar 2026
Posts: 314
Own Kudos:
501
 [1]
Given Kudos: 72
Location: India
Concentration: Strategy, Technology
Schools: IIMA PGPX'23 ISB '23 XLRI
WE:Engineering (Computer Software)
Schools: IIMA PGPX'23 ISB '23 XLRI
Posts: 314
Kudos: 501
 [1]
GMAT Club Around The World!!! What is the remainder when 3^50 is 31 Dec 2021, 11:27
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the remainder when \(3^{50}\) is divided by 7?

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




Happy New Year Nepal

Dec 31 Event: GMAT Club Around The World!
(38 new questions posted every hour time zone on Dec 31!)

Show more


3^50 can be written as (3^3)^16 * 3^2
So, (27^16 * 9) / 7
27 leaves a remainder of -1 with 7 and -1^16 = 1
1*9/7 = 2 remainder. B
avatar
02999
avatar
Joined: 09 Apr 2020
Last visit: 06 May 2023
Posts: 19
Own Kudos:
3
Given Kudos: 516
Posts: 19
Kudos: 3
GMAT Club Around The World!!! What is the remainder when 3^50 is 31 Dec 2021, 11:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Euler of 7 = 6. so 3^6k mod 7 =0.
Left part is - 3^2 mod 7=9 mod 7=2 .
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 19 Apr 2026
Posts: 3,173
Own Kudos:
11,464
Given Kudos: 1,862
Location: India
Concentration: Strategy, Leadership
Posts: 3,173
Kudos: 11,464
GMAT Club Around The World!!! What is the remainder when 3^50 is 31 Dec 2021, 13:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Remainder(\(\frac{3^{50}}{7}\))

Remainder(\(\frac{3^{48}}{7}\)) * Remainder(\(\frac{3^{2}}{7}\))

Remainder(\(\frac{3^{16 * 3} }{7}\)) * Remainder(\(\frac{3^{2}}{7}\))

\(\frac{ - 1 ^{16} }{7}\) * 2

1 * 2

= 2
User avatar
100mitra
User avatar
Joined: 29 Apr 2019
Last visit: 06 Jul 2022
Posts: 707
Own Kudos:
634
 [1]
Given Kudos: 49
Status:Learning
Posts: 707
Kudos: 634
 [1]
GMAT Club Around The World!!! What is the remainder when 3^50 is 01 Jan 2022, 01:35
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
3^50 = 9^25 ÷ 7


9^1=9÷7, leaves remainder 2 ………(1)
9^2=81÷7, leaves remainder 4 ………(2)
9^3=729÷7, leaves remainder 1 …….(3)
9^4=6561÷7, leaves remainder 2 …….(4)
9^5=59049÷7, leaves remainder 4 ……….(5)
9^6=531441÷7, leaves remainder 1 ……..(6)
9^7=4782969÷7, leaves remainder 2 ….(7)

Cyclic number : 3
Thus, 25 ÷ 3 = (reminder 1 < cyclic number)
9^25 = 9^1 when ÷ 7, reminder 2
Option B

Posted from my mobile device
User avatar
DiaPro
User avatar
Joined: 24 Aug 2022
Last visit: 05 May 2024
Posts: 8
Own Kudos:
5
 [2]
Given Kudos: 18
Location: India
Posts: 8
Kudos: 5
 [2]
GMAT Club Around The World!!! What is the remainder when 3^50 is 01 Sep 2023, 10:31
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
3^1 - 3 ————-
3^2 - 9 ————- 9/7 , rem = 2
3^3 - 27 ————- 27/7 , rem = 6
3^4 - 81 ————- 81/7 , rem = 4
3^5 - 243 ————- 243/7 , rem = 2
3^6- 729 ————- 729/7 , rem = 6

So cyclical pattern
So 3^50 corresponds to 3^2 will give rem 2
Op B

Posted from my mobile device
User avatar
Khushe
User avatar
Joined: 26 Jan 2022
Last visit: 16 Oct 2025
Posts: 10
Own Kudos:
1
 [1]
Given Kudos: 251
Location: India
Schools: ISB
Schools: ISB
Posts: 10
Kudos: 1
 [1]
GMAT Club Around The World!!! What is the remainder when 3^50 is 30 Jul 2025, 06:01
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The remainder when divided by 7 will be the following for 3^5, 3^6, 3^7 -

  • 3^5 - 243/7; R = 5
  • 3^6 - 729/7; R = 1
  • 3^7 - 2187/7; R = 3

The negative remainders will be -2, -6 & -4 respectively which is not the same as 5, 1 & 3. Hence, the cyclicity will be 6.


DiaPro
3^1 - 3 ————-
3^2 - 9 ————- 9/7 , rem = 2
3^3 - 27 ————- 27/7 , rem = 6
3^4 - 81 ————- 81/7 , rem = 4
3^5 - 243 ————- 243/7 , rem = 2
3^6- 729 ————- 729/7 , rem = 6

So cyclical pattern
So 3^50 corresponds to 3^2 will give rem 2
Op B

Posted from my mobile device
Show more
User avatar
MegB07
User avatar
Joined: 15 Sep 2022
Last visit: 20 Dec 2025
Posts: 55
Own Kudos:
3
Given Kudos: 42
Location: India
Posts: 55
Kudos: 3
GMAT Club Around The World!!! What is the remainder when 3^50 is 11 Aug 2025, 18:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone tell if my approach is correct?

Since cyclicality of 3 is 4, I divided 40 by 4 leaving 2 as remainder. 3^2 = 9 which I divided by 7 and remainder was 2.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,141
Given Kudos: 105,878
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: 109,822
Kudos: 811,141
GMAT Club Around The World!!! What is the remainder when 3^50 is 12 Aug 2025, 00:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MegB07
Can someone tell if my approach is correct?

Since cyclicality of 3 is 4, I divided 40 by 4 leaving 2 as remainder. 3^2 = 9 which I divided by 7 and remainder was 2.
Show more

The cyclicity you refer to there determines the units digit of 3 in a positive integer power, which will not always work here. For example, if we had 3^5, then 5 gives a remainder of 1 when dividing by 4, and 3^1 divided by 7 gives a remainder of 3. However, the actual remainder when 3^5 is divided by 7 is 5.
Moderators:
Bunuel
Math Expert
109822 posts
Krunaal
Tuck School Moderator
853 posts