Last visit was: 25 Apr 2026, 22:34 It is currently 25 Apr 2026, 22:34
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
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 25 Apr 2026
Posts: 11,229
Own Kudos:
45,021
 [18]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,021
 [18]
What is the hundreds digit of 201^201? 13 Aug 2018, 20:05
1
Kudos
Add Kudos
17
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:

65% (hard)

Question Stats:

57% (02:00) correct 43% (01:31) wrong based on 319 sessions

History

Date
Time
Result
Not Attempted Yet
What is the hundreds digit of \(201^{201}\) ?

(A) 0
(B) 1
(C) 2
(D) 5
(E) 7

New question!!!..­
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
PKN
User avatar
Joined: 01 Oct 2017
Last visit: 11 Oct 2025
Posts: 809
Own Kudos:
1,637
 [5]
Given Kudos: 41
Status:Learning stage
WE:Supply Chain Management (Energy)
Posts: 809
Kudos: 1,637
 [5]
What is the hundreds digit of 201^201? 13 Aug 2018, 23:07
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
sandman13
PKN


pattern of hundreds digit of \((201)^n\):-
2-4-6-8-0
Cyclicity:- 5

PKN, how do you know the pattern is 2-4-6-8-0?

I solved this using binomial expansion.
If you think of 201^201 = (200+1)^201 = 201C0*200^201 + 201C1*200^200 + ... + 201C200*200^1 + 201C201*200^0
^the highlighted term equal 201*200 = 40200
^the highlighted part is the hundreds digit. All other terms will have higher powers and won't contribute to the hundreds term.

Answer: C
Show more

Hi sandman13,
If you observe carefully, We have each of the digit of 201 , lies between 0 and 2 inclusive. On successive powers of 201 from 1 to infinity, the tens digit of 201 decides the hundreds digit(1*any number=that number.no carry forward)). Here the tens digit is zero, hence 0*any number=0 with no carry forward.

Hundreds digit of \(201^1\)=2
Hundreds digit of \(201^2\)= 2+Hundreds digit of \(201^1=2+2=4\)
Hundreds digit of \(201^3\)= 2+Hundreds digit of \(201^2=2+4=6\)
Hundreds digit of \(201^4\)= 2+Hundreds digit of \(201^3=2+6=8\)
Hundreds digit of \(201^5\)= 2+Hundreds digit of \(201^4=2+8=0\)
Hundreds digit of \(201^6\)= 2+Hundreds digit of \(201^5=2+0=2\)
Hundreds digit of \(201^7\)= 2+Hundreds digit of \(201^6=2+2=4\)

This was my approach, it mayn't be a standard one.
General Discussion
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 25 Apr 2026
Posts: 11,229
Own Kudos:
45,021
 [2]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,021
 [2]
What is the hundreds digit of 201^201? 13 Aug 2018, 20:55
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
chetan2u
What is the hundreds digit of \(201^{201}\) ?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 7

New question!!!..
Show more

Apart from cyclicity, we can read this as remainder when divided by 1000..
so \(201^{201}=(200+1)^{201}=200^{201}+.....200^2*1^{199}+200^1*1^200+1^{201}\)
so all terms apart from last two terms will be divisible by 1000..
hence remainder will be \(200^1*1+1=201\)
the hundreds digit therefore will be 2

C
User avatar
PKN
User avatar
Joined: 01 Oct 2017
Last visit: 11 Oct 2025
Posts: 809
Own Kudos:
1,637
 [2]
Given Kudos: 41
Status:Learning stage
WE:Supply Chain Management (Energy)
Posts: 809
Kudos: 1,637
 [2]
What is the hundreds digit of 201^201? Updated on: 13 Aug 2018, 21:24
Originally posted by PKN on 13 Aug 2018, 21:08.
Last edited by PKN on 13 Aug 2018, 21:24, edited 1 time in total.
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
chetan2u
chetan2u
What is the hundreds digit of \(201^{201}\) ?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 7

New question!!!..
Show more

pattern of hundreds digit of \((201)^n\):-
2-4-6-8-0
Cyclicity:- 5

We have \(\frac{201}{5}\) leaves 1 as remainder.
So, hundreds digit of \((201)^{201}\) is same as hundreds digit of \((201)^1\).

Therefore, the required hundreds digit is 2.

Ans. (C)
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,800
Own Kudos:
6,235
 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,800
Kudos: 6,235
 [1]
What is the hundreds digit of 201^201? 13 Aug 2018, 21:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
What is the hundreds digit of \(201^{201}\) ?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 7

New question!!!..
Show more

\((201)^0\) - Hundred's digit is 0
\((201)^1\) - Hundred's digit is 2
\((201)^2\) - Hundred's digit is 4
\((201)^3\) - Hundred's digit is 6
\((201)^4\) - Hundred's digit is 8
\((201)^5\) - Hundred's digit is 0
\((201)^6\) - Hundred's digit is 2
\((201)^7\) - Hundred's digit is 4

A pattern emerges and 8 is the hundred's digit for the 4,9,14,19.......199th power of 201.

Therefore, the hundred's digit of \(201^{201}\) is 2(Option C)
User avatar
sandman13
User avatar
Joined: 20 Apr 2018
Last visit: 26 Dec 2019
Posts: 132
Own Kudos:
304
 [1]
Given Kudos: 156
Concentration: Technology, Nonprofit
Schools: ISB '21 (A)
WE:Analyst (Non-Profit and Government)
Schools: ISB '21 (A)
Posts: 132
Kudos: 304
 [1]
What is the hundreds digit of 201^201? 13 Aug 2018, 22:42
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PKN
chetan2u
chetan2u
What is the hundreds digit of \(201^{201}\) ?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 7

New question!!!..

pattern of hundreds digit of \((201)^n\):-
2-4-6-8-0
Cyclicity:- 5
Show more

PKN, how do you know the pattern is 2-4-6-8-0?

I solved this using binomial expansion.
If you think of 201^201 = (200+1)^201 = 201C0*200^201 + 201C1*200^200 + ... + 201C200*200^1 + 201C201*200^0
^the highlighted term equal 201*200 = 40200
^the highlighted part is the hundreds digit. All other terms will have higher powers and won't contribute to the hundreds term.

Answer: C
avatar
umabharatigudipalli
avatar
Joined: 21 Jan 2017
Last visit: 22 Sep 2018
Posts: 27
Own Kudos:
6
Given Kudos: 45
Posts: 27
Kudos: 6
What is the hundreds digit of 201^201? 21 Aug 2018, 04:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
What is the hundreds digit of \(201^{201}\) ?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 7

New question!!!..
Show more

The answer is (c)2.

My approach might be lengthy yet easy! Here it goes.

Note: 401, 601 etc are all the last 3 digits

\(201^{201}\) can be written as \(201^{200}\) * 201.
= \((201^{2})^{100}\) * 201
= \((401)^{100}\) * 201
= \((401^{2})^{50}\) * 201
= \(801^{50}\) * 201
= \(((801)^{2})^{25}\) * 201
= \((601)^{25}\) *201
= \((601^{2})^{12}\) * 201 * 601
= \((201)^{12}\) *201 * 601
= \(((201)^{2})^{6}\) *201 *601

again \(201^2\) is 401 hence substitute,
\(401^2\) is 801
= 601 * 801 * 201 * 601
the hundreds digit of the above is 2.

Thanks,
Uma
User avatar
Apeksha2101
User avatar
Joined: 31 May 2018
Last visit: 06 Jun 2025
Posts: 41
Own Kudos:
10
Given Kudos: 28
Posts: 41
Kudos: 10
What is the hundreds digit of 201^201? 30 May 2024, 04:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pushpitkc
chetan2u
What is the hundreds digit of \(201^{201}\) ?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 7

New question!!!..

\((201)^0\) - Hundred's digit is 0
\((201)^1\) - Hundred's digit is 2
\((201)^2\) - Hundred's digit is 4
\((201)^3\) - Hundred's digit is 6
\((201)^4\) - Hundred's digit is 8
\((201)^5\) - Hundred's digit is 0
\((201)^6\) - Hundred's digit is 2
\((201)^7\) - Hundred's digit is 4

A pattern emerges and 8 is the hundred's digit for the 4,9,14,19.......199th power of 201.

Therefore, the hundred's digit of \(201^{201}\) is 2(Option C)
Show more


I do understand your answer, but calculating hundred's for these numbers to understand the cyclicity will be time taking process in exam, wouldn't it take som much of time
User avatar
Oppenheimer1945
User avatar
Joined: 16 Jul 2019
Last visit: 21 Apr 2026
Posts: 784
Own Kudos:
664
Given Kudos: 236
Location: India
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80
GPA: 7.81
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80
Posts: 784
Kudos: 664
What is the hundreds digit of 201^201? 15 Jun 2024, 07:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(200+1)^201
As all terms except last 2 has huge no of zeros let’s
Focus on last 2 terms:
201C200 (200)+201C201 .1
=40200+1

We get 2

Posted from my mobile device
Moderators:
Bunuel
Math Expert
109830 posts
Krunaal
Tuck School Moderator
852 posts