Last visit was: 04 Sep 2026, 09:24 It is currently 04 Sep 2026, 09:24
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
User avatar
fitzpratik
User avatar
Joined: 17 Oct 2016
Last visit: 08 Mar 2021
Posts: 224
Own Kudos:
510
Given Kudos: 49
Location: India
Concentration: General Management, Healthcare
Schools: Owen '22 (I) Boston U '22 (A$) Jones '22 (WL) Kenan-Flagler '22 (WA) Olin '22 (WA$)
GPA: 3.05
WE:Pharmaceuticals (Healthcare/Pharmaceuticals)
Products:
My Reviews
Schools: Owen '22 (I) Boston U '22 (A$) Jones '22 (WL) Kenan-Flagler '22 (WA) Olin '22 (WA$)
Posts: 224
Kudos: 510
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479? Updated on: 10 Aug 2017, 00:55
Originally posted by fitzpratik on 09 Aug 2017, 19:51.
Last edited by Bunuel on 10 Aug 2017, 00:55, edited 2 times in total.
Renamed the topic.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

72% (01:34) correct 28% (00:59) wrong based on 25 sessions

History

Date
Time
Result
Not Attempted Yet
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479?

A. 0

B. 1

C. 2

D. 5

E. 8



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
ShowHide Answer
Official Answer
A
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 04 Sep 2026
Posts: 11,288
Own Kudos:
46,085
 [1]
Given Kudos: 339
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
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,288
Kudos: 46,085
 [1]
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479? 09 Aug 2017, 23:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fitzpratik
What is the units digit of 314673^2 × 976452^3 × (32168^5 + 865^2)^479?

A. 0

B. 1

C. 2

D. 5

E. 8
Show more


Hi...
Relook at the Q and choices, 0 can never be the units digit here..

For ANSWER let's see only the units digit..
\(3^2*2^3*(8^5+5^2)^{479}\)
... This means \(9*8*(8+5)^{480-1}\)
480 is div by 4 so units digit of base will be same as that of 4-1 or 3..
So 72*13^3.....2*3^3=2*7=14..
Units digit is 4
User avatar
fitzpratik
User avatar
Joined: 17 Oct 2016
Last visit: 08 Mar 2021
Posts: 224
Own Kudos:
510
Given Kudos: 49
Location: India
Concentration: General Management, Healthcare
Schools: Owen '22 (I) Boston U '22 (A$) Jones '22 (WL) Kenan-Flagler '22 (WA) Olin '22 (WA$)
GPA: 3.05
WE:Pharmaceuticals (Healthcare/Pharmaceuticals)
Products:
My Reviews
Schools: Owen '22 (I) Boston U '22 (A$) Jones '22 (WL) Kenan-Flagler '22 (WA) Olin '22 (WA$)
Posts: 224
Kudos: 510
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479? 09 Aug 2017, 23:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
fitzpratik
What is the units digit of 314673^2 × 976452^3 × (32168^5 + 865^2)^479?

A. 0

B. 1

C. 2

D. 5

E. 8


Hi...
Relook at the Q and choices, 0 can never be the units digit here..

For ANSWER let's see only the units digit..
\(3^2*2^3*(8^5+5^2)^{479}\)
... This means \(9*8*(8+5)^{480-1}\)
480 is div by 4 so units digit of base will be same as that of 4-1 or 3..
So 72*13^3.....2*3^3=2*7=14..
Units digit is 4
Show more

Hi chetan2u

Have made necessary changes!

Please do excuse my clumsiness.

Thank you.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 04 Sep 2026
Posts: 11,288
Own Kudos:
46,085
Given Kudos: 339
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
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,288
Kudos: 46,085
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479? 10 Aug 2017, 00:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fitzpratik
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479?

A. 0

B. 1

C. 2

D. 5

E. 8
Show more


For ANSWER let's see only the units digit..
\(7^{32}*5^{23}*(8^5+2)^{479}\)
... This means \(7^4*5*(8^1+2)^{480-1}\)......
after every 4th power, the units digit repeat
for units digit 0, 1, 5 and 6... it remains the same for every positive integer power
for 2,3,7,8 it repeats after every 4th.. so 2^401 will be same as 2^(4*50+1) or 2^1
4 and 9 repeat after every second..
so \(7^4*5\) will be 5 as ODD *5 will have units digit 5
but \((8^1+2)^{479} = 10^{479}\) will always have 0 as units digit..
so overall also it will be 0

A
User avatar
fitzpratik
User avatar
Joined: 17 Oct 2016
Last visit: 08 Mar 2021
Posts: 224
Own Kudos:
510
Given Kudos: 49
Location: India
Concentration: General Management, Healthcare
Schools: Owen '22 (I) Boston U '22 (A$) Jones '22 (WL) Kenan-Flagler '22 (WA) Olin '22 (WA$)
GPA: 3.05
WE:Pharmaceuticals (Healthcare/Pharmaceuticals)
Products:
My Reviews
Schools: Owen '22 (I) Boston U '22 (A$) Jones '22 (WL) Kenan-Flagler '22 (WA) Olin '22 (WA$)
Posts: 224
Kudos: 510
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479? 10 Aug 2017, 01:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
fitzpratik
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479?

A. 0

B. 1

C. 2

D. 5

E. 8


For ANSWER let's see only the units digit..
\(7^{32}*5^{23}*(8^5+2)^{479}\)
... This means \(7^4*5*(8^1+2)^{480-1}\)......
after every 4th power, the units digit repeat
for units digit 0, 1, 5 and 6... it remains the same for every positive integer power
for 2,3,7,8 it repeats after every 4th.. so 2^401 will be same as 2^(4*50+1) or 2^1
4 and 9 repeat after every second..
so \(7^4*5\) will be 5 as ODD *5 will have units digit 5
but \((8^1+2)^{479} = 10^{479}\) will always have 0 as units digit..
so overall also it will be 0

A
Show more

Could not have put it in any better way!!
User avatar
generis
User avatar
Senior SC Moderator
Joined: 22 May 2016
Last visit: 18 Jun 2022
Posts: 5,255
Own Kudos:
38,002
Given Kudos: 9,464
Expert
Expert reply
Posts: 5,255
Kudos: 38,002
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479? 11 Aug 2017, 07:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
fitzpratik
What is the units digit of 31467^32 × 97645^23 × (32168^5 + 8652)^479?

A. 0

B. 1

C. 2

D. 5

E. 8


For ANSWER let's see only the units digit..
\(7^{32}*5^{23}*(8^5+2)^{479}\)
... This means \(7^4*5*(8^1+2)^{480-1}\)......
after every 4th power, the units digit repeat
for units digit 0, 1, 5 and 6... it remains the same for every positive integer power
for 2,3,7,8 it repeats after every 4th.. so 2^401 will be same as 2^(4*50+1) or 2^1
4 and 9 repeat after every second..
so \(7^4*5\) will be 5 as ODD *5 will have units digit 5
but \((8^1+2)^{479} = 10^{479}\) will always have 0 as units digit..
so overall also it will be 0

A
Show more
chetan2u , I'm not clear about why you wrote this part: \((8^1+2)^{480-1}\). (480/4) is evenly divisible, maybe the (-1) is a negative remainder (and I will never understand negative remainders fully) but that doesn't seem to explain the exponent manipulation, either. . .

Was it to show remainder in case \((8^1+2)\) summed to something other than zero? If that is the reason, I still don't follow.

You can't distribute the exponent, so cyclicity of four for addends 8 and 2 can't be the reason.

And cyclicity per se doesn't seem to be the reason: 2, 3, 7, and 8 have cyclicity of four (where 480 is divisible by 4) - but 0, 1, 4, 5, 6, and 9 do not have cyclicity of four. That 8 might have had units digit 2, e.g. Then units digit is 4, and I can't see how \(4^{480-1}\) helps.

The (-1) part isn't clear, either. I suppose I know that, in the number whose cyclicity of powers is four, I can take the \(n^4\) term and "move backwards" by one power in the cycle to get the units digit, but 479/4 leaves remainder 3, which is the same thing as "moving one place backward" in the cycle. It seems harder to see, from a divisibility perspective, that (-1) power in cycle = (+3) power in cycle.

I looked only at \(8^5\), where 5/4 = remainder 1, units digit of first term is same as \(8^1\) = 8. Last digit of addend in parentheses is 2. (8 + 2) = 0.

And as you point out, zero to any power (except zero) is 0. So I just wrote (first expression) * 0.

Sorry if this confusion arises because I am missing something obvious. I suspect what you wrote is important for problems different from this one. Please explain?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
Bunuel
Math Expert
113129 posts