Last visit was: 20 Nov 2025, 07:59 It is currently 20 Nov 2025, 07:59
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
605-655 Level|   Exponents|   Remainders|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,420
Own Kudos:
778,535
 [5]
Given Kudos: 99,987
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: 105,420
Kudos: 778,535
 [5]
If x and y are positive integers and r is the remainder when 3^(4x+2) 05 Oct 2020, 07:45
Kudos
Add Kudos
5
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:

45% (medium)

Question Stats:

59% (01:23) correct 41% (01:41) wrong based on 226 sessions

History

Date
Time
Result
Not Attempted Yet
If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1
ShowHide Answer
Official Answer
B
avatar
GowriPrakash
avatar
Current Student
Joined: 28 Dec 2019
Last visit: 06 Jun 2024
Posts: 13
Own Kudos:
7
 [1]
Given Kudos: 21
Location: India
Schools: Schulich Jan '23 (I) Schulich Sept '23 (A)
GMAT 1: 690 Q48 V36
Schools: Schulich Jan '23 (I) Schulich Sept '23 (A)
GMAT 1: 690 Q48 V36
Posts: 13
Kudos: 7
 [1]
If x and y are positive integers and r is the remainder when 3^(4x+2) 05 Oct 2020, 08:04
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x and y are positive integers and r is the remainder when \(3^{4x + 2}\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1
Show more


Is the equation \(3^{4x + 2}\) right ? Because there is no y in it.
avatar
ah1028
avatar
Joined: 17 Sep 2020
Last visit: 30 Mar 2022
Posts: 7
Own Kudos:
2
Given Kudos: 23
Location: United States
Schools: Stern '24 (S) Fuqua '24 (II)
GMAT 1: 680 Q47 V35
GPA: 3.3
Schools: Stern '24 (S) Fuqua '24 (II)
GMAT 1: 680 Q47 V35
Posts: 7
Kudos: 2
If x and y are positive integers and r is the remainder when 3^(4x+2) 05 Oct 2020, 08:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GowriPrakash
Bunuel
If x and y are positive integers and r is the remainder when \(3^{4x + 2}\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1


Is the equation \(3^{4x + 2}\) right ? Because there is no y in it.
Show more

Agreed...if that is truly the equation then A. If you know x=25 then you would be able to figure out the value of 3^(4x+2) and solve for the remainder r.
avatar
livfcind
avatar
Joined: 03 Aug 2019
Last visit: 29 Mar 2022
Posts: 62
Own Kudos:
80
Given Kudos: 170
Location: India
Concentration: Operations, Strategy
GPA: 4
WE:Operations (Aerospace and Defense)
Posts: 62
Kudos: 80
If x and y are positive integers and r is the remainder when 3^(4x+2) 05 Oct 2020, 08:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x and y are positive integers and r is the remainder when 34x+234x+2 is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1

Bunuel kindly recheck the question as with given stem you don't need either S1 or S2 to answer the question.There is something wrong with the original question part.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,420
Own Kudos:
778,535
Given Kudos: 99,987
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: 105,420
Kudos: 778,535
If x and y are positive integers and r is the remainder when 3^(4x+2) 05 Oct 2020, 09:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1
Show more

Fixed the question. It's - If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 20 Nov 2025
Posts: 8,423
Own Kudos:
4,982
 [1]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,423
Kudos: 4,982
 [1]
If x and y are positive integers and r is the remainder when 3^(4x+2) 05 Oct 2020, 09:39
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1
Show more

cyclicity of 3 ; 3,9,7,1
given \(3^{4x + 2}+y\) is divided by 10 remainder r is left determine its value
#1
x=25
we see that \(3^{4x + 2}+y\) the value of 3^4x+2 would always give unit digit as 9 ; so its value of y which is important to know unit digit of expression ; insufficient
#2
y=1
we see that the unit digit is 0 ; hence r is 0
sufficient
option B
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 20 Nov 2025
Posts: 5,794
Own Kudos:
5,515
Given Kudos: 161
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,794
Kudos: 5,515
If x and y are positive integers and r is the remainder when 3^(4x+2) 05 Oct 2020, 09:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Asked: If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25
3^{102} + y mod 10 = (9+y)mod10
NOT SUFFICIENT

(2) y = 1
9*3^{4x} + y mod 10 = (9+y)mod10 = 10mod10 = 0
SUFFICIENT

IMO B
User avatar
Basshead
User avatar
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 925
Own Kudos:
302
Given Kudos: 432
Location: United States
Posts: 925
Kudos: 302
If x and y are positive integers and r is the remainder when 3^(4x+2) 28 Oct 2020, 04:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Cyclicity of 3: 3, 9, 7, 1

If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25

We don't know the value of y; insufficient.

(2) y = 1

We can determine that 4x + 2 is 2 more than a multiple of 4; thus, 3^{4x+2} has a units digit of 9 and y = 1.

9 + 1 = 10.
10/10 = remainder 0.

Statement 2 is sufficient. Answer is B.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,600
Own Kudos:
1,079
Posts: 38,600
Kudos: 1,079
If x and y are positive integers and r is the remainder when 3^(4x+2) 07 Apr 2025, 06:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105420 posts
kingbucky
496 posts