What is the tens digit of 36^10? A. 1 B. 3 C. 5 D. 7 E. 9

We need to find the tens digit of 36^10 36^10 = (6^2)^10 = 6^(2*10) = 6^20 Last Two digits of 6 follow following pattern Last Two Digits of 6^1 = 06 Last Two Digits of 6^2 = 36 Last Two Digits of 6^3 = 36*6 = 16 Last Two Digits of 6^4 = 16*6 = 96 Last Two Digits of 6^5 = 96*6 = 76 Last Two Digits of 6^6 = 76*6 = 56 Last Two Digits of 6^7 = 56*6 = 36 Last Two Digits of 6^8 = 36*6 = 16 => So, from 6^2 cycle of tens' digit repeats as 3, 1, 9, 7 , 5, 3, 1 9, 7 , 5 => We have a cycle of 5 from the 2nd term => Tens' digit of 6^20 = Now 20 = 1(6^1 not part of cycle) + 15 (cycle of 5*3) + 4 (as cycle starts from 2nd term) = Fourth term of the cycle = 7 So, Answer will be D Hope it helps! Link to Theory for Last Two digits of exponents here . Link to Theory for Units' digit of exponents here .

Last visit was: 24 Apr 2026, 12:14

It is currently 24 Apr 2026, 12:14

Toolkit

Quantitative Questions

Problem Solving (PS)

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

Request Expert Reply

Confirm Cancel

Apr 26
Score High on the GMAT with Target Test Prep
10:00 AM EDT
-
11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 27
Try OnDemand GMAT Masterclass
11:00 AM EDT
-
12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 28
Join - GMAT Day!
08:00 AM PDT
-
11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.

Back to Forum

Create Topic

What is the tens digit of 36^10?

1 2

Maria240895chile

Joined: 23 Apr 2021

Last visit: 07 Jun 2023

Posts: 115

Own Kudos:

Given Kudos: 115

Posts: 115

Kudos: 59

11 Apr 2023, 06:43

Kudos

Bookmarks

multiply omitting numbers before tens
a) 36*36=...96
b) 96*36=...56
c) 56*36=...16
d) 16*36=...76
e) 76*36=...36

we have used 6 out of 10 thirty six, and no the pattern starts to repeat it self ending in letter d) when tens digit is 7

KB1920

Joined: 20 May 2023

Last visit: 13 Feb 2026

Posts: 5

Own Kudos:

Posts: 5

Kudos: 1

10 May 2024, 23:22

Kudos

Bookmarks

Just want to add one observation
the pattern is 3, 1, 9, 7, 5, 3, 1, 9, 7, 5, 3, 1, 9, 7, 5, 3, 1, 9, 7 there is a constant difference of 8
3+8=11(1) 11+8=19 (9) 19+8=27(7) 27+8=35(5) 35+8=43(3)
The tens digit, then, will be 7.

Adarsh_24

Joined: 06 Jan 2024

Last visit: 03 Apr 2025

Posts: 240

Own Kudos:

Given Kudos: 2,015

Posts: 240

Kudos: 65

06 Sep 2024, 07:55

Kudos

Bookmarks

Quote:

When we multiply -4*-4=16..
And 16*16=...56
Nowfifth -4 is left..
When 56 is multiplied by -4, we get -24 as last two digits..
But remainder cannot be NEGATIVE, so add to 100..
100+(-24)=76

we are taking only 2 digits at each power when (-4)^5
As ..56
..24

Is it deliberately done and is it because our divisor is 100 and remainder should be less than divisor.

because if we actually done the calculation , we'll get -1024 and I can't really put my finger on what to do next to get it to a positive remainder.

BrushMyQuant

Tutor

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 Verified score

GPA: 3

WE:Information Technology (Computer Software)

Expert

Expert reply

Schools: XLRI (A)

GMAT 1: 700 Q51 V31 Verified score

Posts: 2,286

Kudos: 2,680

Updated on: 03 Oct 2024, 07:42

Originally posted by BrushMyQuant on 13 Sep 2024, 21:28.
Last edited by BrushMyQuant on 03 Oct 2024, 07:42, edited 1 time in total.

Kudos

Bookmarks

We need to find the tens digit of 36^10

36^10 = (6^2)^10 = 6^(2*10) = 6^20

Last Two digits of 6 follow following pattern

Last Two Digits of 6^1 = 06
Last Two Digits of 6^2 = 36
Last Two Digits of 6^3 = 36*6 = 16
Last Two Digits of 6^4 = 16*6 = 96
Last Two Digits of 6^5 = 96*6 = 76
Last Two Digits of 6^6 = 76*6 = 56
Last Two Digits of 6^7 = 56*6 = 36 [ same as 6^2 ]
Last Two Digits of 6^8 = 36*6 = 16 [ same as 6^3 ]

=> So, from 6^2 cycle of tens' digit repeats as 3, 1, 9, 7 , 5, 3, 1 9, 7 , 5
=> We have a cycle of 5 from the 2nd term
=> Tens' digit of 6^20 = Now 20 = 1(6^1 not part of cycle) + 15 (cycle of 5*3) + 4 (as cycle starts from 2nd term) = Fourth term of the cycle = 7

So, Answer will be D
Hope it helps!

Link to Theory for Last Two digits of exponents here.

Link to Theory for Units' digit of exponents here.

Akshaynandurkar

Joined: 29 Apr 2023

Last visit: 19 Jan 2025

Posts: 69

Own Kudos:

Given Kudos: 104

Location: India

GMAT Focus 1: 635 Q84 V86 DI74 Verified score

Posts: 69

Kudos: 33

21 Sep 2024, 04:28

Kudos

Bookmarks

Look for the cyclicity patterns in this question.
6,36,216,1296,7776, ---56, ---36,---1,...
here leaving first number 6 , cycle repeats as 3,1,9,7,5 (5 nos)
so we have 6^10
means we have total 9 powers (leaving first number)
Remainder of 9/5 = 4
4th tens number is 7