by: WA
23 mins
Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 1712:30 AM EDT
-01:30 AM EDT
Thought your job leaves no time for GMAT prep? After multiple GMAT attempts and a demanding consulting job, Kshitij improved to 695 in under 2 months. Learn the mindset shifts, study strategy, and execution changes that made the breakthrough possible.
Sep 1801:30 AM EDT
-02:30 AM EDT
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Sep 1808:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
Posts: 6,727
Updated on: 13 Nov 2019, 16:16
Originally posted by BrentGMATPrepNow on 09 Apr 2017, 06:49.
Last edited by BrentGMATPrepNow on 13 Nov 2019, 16:16, edited 2 times in total.
Last edited by BrentGMATPrepNow on 13 Nov 2019, 16:16, edited 2 times in total.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:37) correct
29%
(01:53)
wrong
based on 590
sessions
History
Date
Time
Result
Not Attempted Yet
What is the units digit of the product \((32^{28})(33^{47})(37^{19})\)?
A) 0
B) 2
C) 4
D) 6
E) 8
Hint:
*kudos for all correct solutions
A) 0
B) 2
C) 4
D) 6
E) 8
Hint:
There’s a fast approach and a slow approach
*kudos for all correct solutions
Every tricky question should trigger a follow up quiz.
Build that habit with
GMAT Club Forum Quiz →.
Posts: 6,727
Updated on: 29 Sep 2020, 12:06
Originally posted by BrentGMATPrepNow on 10 Apr 2017, 07:55.
Last edited by BrentGMATPrepNow on 29 Sep 2020, 12:06, edited 1 time in total.
Last edited by BrentGMATPrepNow on 29 Sep 2020, 12:06, edited 1 time in total.
GMATPrepNow
-----ASIDE-----------------------------------------
There are some "nice" numbers that, when raised to various powers, ALWAYS have the same units digit.
For example, the units digit of 70^n will be 0 FOR ALL POSITIVE INTEGER VALUES OF N
Likewise, the units digit of 91^n will be 1 FOR ALL POSITIVE INTEGER VALUES OF N
And the units digit of 86^n will be 6 FOR ALL POSITIVE INTEGER VALUES OF N
-----NOW ONTO THE QUESTION-----------------
Notice that the exponent 47 is equal to the SUM of the other two exponents (28 and 19)
So, it might be useful to take 33^47 and REWRITE it as (33^28)(33^19)
NOTE: later on, we'll apply a nice exponent rule that says "(a^n)(b^n) = (ab)^n"
We get: (32^28)(33^47)(37^19) = (32^28)(33^28)(33^19)(37^19)
= (32^28 x 33^28)(33^19 x 37^19)
= (32 x 33)^28 (33 x 37)^19 [applied above rule]
=(---6)^28 (---1)^19 [I'm focusing solely on the units of each product. So, I use "---" to represent the other digits]
=(----6)(----1) [When ----6 is raised to any power the units digit is always 6. The same applies to ----1]
= -------6
Answer:
RELATED VIDEOS
32^28
for powers of 32, the units digit follows the pattern (^power - units digit):
^1 - 2
^2 - 4
^3 - 8
^4 - 6
^5 - 2 and the pattern repeats, every 4 powers
we are looking for the 28th power, 28/4 = 7 R0, therefore we use the 4th place in the pattern --> 6
33^47
for powers of 33, the units digit follows the pattern (^power - units digit):
^1 - 3
^2 - 9
^3 - 7
^4 - 1
^5 - 3 and the pattern repeats, every 4 powers
we are looking for the 47th power, 47/4 = 11 R3, therefore we use the 3rd place in the pattern --> 7
37^19
for powers of 37, the units digit follows the pattern (^power - units digit):
^1 - 7
^2 - 9
^3 - 3
^4 - 1
^5 - 7 and the pattern repeats, every 4 powers
we are looking for the 19th power, 19/4 = 4 R3, therefore we use the 3rd place in the pattern --> 3
6 x 7 x 3 =126 and the answer is D) 6
for powers of 32, the units digit follows the pattern (^power - units digit):
^1 - 2
^2 - 4
^3 - 8
^4 - 6
^5 - 2 and the pattern repeats, every 4 powers
we are looking for the 28th power, 28/4 = 7 R0, therefore we use the 4th place in the pattern --> 6
33^47
for powers of 33, the units digit follows the pattern (^power - units digit):
^1 - 3
^2 - 9
^3 - 7
^4 - 1
^5 - 3 and the pattern repeats, every 4 powers
we are looking for the 47th power, 47/4 = 11 R3, therefore we use the 3rd place in the pattern --> 7
37^19
for powers of 37, the units digit follows the pattern (^power - units digit):
^1 - 7
^2 - 9
^3 - 3
^4 - 1
^5 - 7 and the pattern repeats, every 4 powers
we are looking for the 19th power, 19/4 = 4 R3, therefore we use the 3rd place in the pattern --> 3
6 x 7 x 3 =126 and the answer is D) 6
General Discussion
Posts: 6,727
That's a valid approach, amynicole.
There's another approach that's much faster. Can you spot it?
Hint:
Cheers,
Brent
There's another approach that's much faster. Can you spot it?
Hint:
notice that the largest exponent is equal to the sum of the other two exponents
Cheers,
Brent
GMATPrepNow
Hi Brent,
How does "notice that the largest exponent is equal to the sum of the other two exponents" Helps? All(2, 3, 7, 8) the 3 numbers have cycle of 4 repetitions.
Thanks
Nandish
old1guy
Joined: 18 Feb 2017
Last visit: 05 Jan 2018
Posts: 8
Location: United States
Schools: Anderson (UCLA)
GMAT 1: 730 Q47 V42
GPA: 3.95
GMATPrepNow
I also solved it by using cycle and took me around 2:30 minutes
But this hint is genius
32^28 * 33^47 * 37^19 = (32^28 * 33^28 )*(33^19 * 37 ^19) == (32 *33)^28 * [Rest Does not matter] as 6 has cycle of 1 and unit digit will always be 6.
Kudos to GMATPrepNow
gmathopeful19
Joined: 09 Oct 2016
Last visit: 27 Jun 2018
Posts: 65
Location: United States
Schools: Kellogg '20 (A) (A$) Tuck '20 (WL) Duke '20 (I)
GMAT 1: 740 Q49 V42
GPA: 3.49
Products:
Wow! This is cool. I did it the long way...hopefully I can remember this on the test
Posted from my mobile device
Posted from my mobile device
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,878
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,878
GMATPrepNow
Cyclicity of number 2 = 4
So, \(32^{28}\) will have units digit 6
Cyclicity of number 3 = 4
So, \(33^{47} = 33^{44+3}\) will have units digit 7
Cyclicity of number 7 = 4
So, \(37^{19} = 37^{16+3}\) will have units digit 3
Thus, the units digit of \(32^{28}*33^{47}*37^{19} = 6*7*3 = 6\); Answer will be (D) 6
_________________
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,878
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,878
BrentGMATPrepNow
\(2^4 = 6\)
So, \(32^{28} = 2^{140} = 2^{4*35} = \)Units digit \(6\)
\(3^4 = 1\) & \(3^3 = 7\)
So, \(33^{47} = 33^{4*11+3} = 1*7 =\) units digit \(7\)
\(7^4 = 1\) & \(7^3 = 3\)
So, \(37^{19} = 37^{4*4+3} =\) Units digit 3
Thus, units digit is \(6*7*3 = 6\), Answer is (D)
_________________
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.
_________________
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.
_________________
Moderator:
Announcements
Monday, Sep 14, 2026
11:30am NY / 3:30pm London / 9pm Mumbai
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.