Last visit was: 18 Nov 2025, 14:09 It is currently 18 Nov 2025, 14:09
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
705-805 Level|   Exponents|   Remainders|         
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,062
 [7]
Given Kudos: 99,964
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: 105,355
Kudos: 778,062
 [7]
HOT Competition 26 Aug/8AM: What is the units digit of n^(p+1), where 26 Aug 2020, 08:00
Kudos
Add Kudos
7
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:

75% (hard)

Question Stats:

48% (01:50) correct 52% (02:07) wrong based on 428 sessions

History

Date
Time
Result
Not Attempted Yet
What is the units digit of \(n^{(p+1)}\), where n is a positive integer and p is a prime number greater than 3?

(1) When p is divided by 3, the remainder is 2.
(2) When n is divided by 10, the tenths digit of the resulting number is 9.



 

This question was provided by GMATWhiz
for the Heroes of Timers Competition

 

ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 18 Nov 2025
Posts: 6,835
Own Kudos:
16,349
 [5]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,835
Kudos: 16,349
 [5]
HOT Competition 26 Aug/8AM: What is the units digit of n^(p+1), where 26 Aug 2020, 08:18
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer: Option B

Please check the video for the step-by-step solution.

GMATinsight's Solution



Attachment:
Screenshot 2020-08-26 at 8.45.49 PM.png
Screenshot 2020-08-26 at 8.45.49 PM.png [ 1.02 MiB | Viewed 6284 times ]
General Discussion
User avatar
Saupayan
User avatar
Joined: 30 May 2013
Last visit: 23 May 2025
Posts: 108
Own Kudos:
137
 [3]
Given Kudos: 94
Status:Full-time employee
Affiliations: Apple Inc
Location: United States
Saupayan: Mazumdar
Concentration: Economics, Leadership
GMAT 1: 760 Q51 V41
GRE 1: Q170 V160
GPA: 3.89
WE:Engineering (Computer Hardware)
GMAT 1: 760 Q51 V41
GRE 1: Q170 V160
Posts: 108
Kudos: 137
 [3]
HOT Competition 26 Aug/8AM: What is the units digit of n^(p+1), where 26 Aug 2020, 08:10
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
What is the units digit of n^(p+1), where n is a positive integer and p is a prime number greater than 3?

(1) When p is divided by 3, the remainder is 2.
(2) When n is divided by 10, the tenths digit of the resulting number is 9.
Show more

(1) tells us about the power. p can be 5 or 11 (or someother number, i didn't need to calculate). But without knowing anything about n, we can't say what n^(p+1) will be. So, it's not sufficient
(2) the tenths digit of n/10 is the unit digit of n. So, units digit of n is 9.
9^(anything odd) --> units digit is 9
9^(anything even) --> units digit is 1

Now, you may think this isn't sufficient, but let's look again.

We know p is a prime number > 3, so p has to be odd.
=> p+1 has to be even
so, we can determine exactly what the unit digit of 9^(even number) will be.

Hence statement 2 alone is sufficient. Answer B
avatar
Shokhrukh22
avatar
Joined: 04 Jan 2016
Last visit: 23 Sep 2020
Posts: 4
Own Kudos:
27
 [2]
Given Kudos: 8
Location: Uzbekistan
GMAT 1: 680 Q49 V33
GPA: 3.72
WE:Analyst (Consulting)
GMAT 1: 680 Q49 V33
Posts: 4
Kudos: 27
 [2]
HOT Competition 26 Aug/8AM: What is the units digit of n^(p+1), where 26 Aug 2020, 23:55
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1: When p is divided by 3, the remainder is 2. - This statement is clearly insufficient, because it gives information only about p. We don't know anything about n from this statement.

Statement 2: When n is divided by 10, the tenths digit of the resulting number is 9. - Since the tenth digit of the resulting number is 9, we can be sure that the last digit of n is equal to 9. Now let's try some numbers. 9^1=9, 9^2=81, 9^3=9, 9^4=1. From this it is clear that the units digit of n will be 9 if p+1 is odd and 1 if p+1 is even. Since it is given that p is a prime number greater than 3, p+1 is even number. So the units digit of n^(p+1) is equal to 1. Sufficient. Answer is B.
Moderators:
Bunuel
Math Expert
105355 posts
kingbucky
496 posts