Last visit was: 10 Jul 2025, 01:19 It is currently 10 Jul 2025, 01:19
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
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 09 Jul 2025
Posts: 11,295
Own Kudos:
41,643
 [16]
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,295
Kudos: 41,643
 [16]
What is the remainder when x^2y is divided by 10? 28 Jul 2018, 00:34
2
Kudos
Add Kudos
14
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
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:

36% (01:16) correct 64% (01:04) wrong based on 171 sessions

History

Date
Time
Result
Not Attempted Yet
What is the remainder when \(x^{2y}\) is divided by 10?

(1) x=9
(2) y=2

Chetan's questions
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 09 Jul 2025
Posts: 11,295
Own Kudos:
41,643
 [7]
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,295
Kudos: 41,643
 [7]
What is the remainder when x^2y is divided by 10? 28 Jul 2018, 01:02
7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
axmanX
(Statement 1) x=9

when y is unknown, assuming even a positive value of y,

when y=1, x^2y=81, rem=1
when y=2, x^2y=6561, rem=1

Answer: A

you missed out y as fraction..

\(x^2y\) divided by 10 MEANS units digit of x^2y

1) x=9..
if y is integer, units digit will always be 1
if y is a fraction say 1/2, units digit will be 9
insuff

2) y = 2
will depend on x
x is 1, ans is 1
x is 2 ans is 6
insuff

combined
ans is 1
suff

C

NOTE - always work for integer and fraction and 0 unless specified
General Discussion
avatar
axmanX
avatar
Joined: 08 Jul 2018
Last visit: 16 Jun 2020
Posts: 23
Own Kudos:
20
Given Kudos: 43
Location: India
Concentration: General Management, Marketing
GPA: 4
Products:
My Reviews
Posts: 23
Kudos: 20
What is the remainder when x^2y is divided by 10? 28 Jul 2018, 00:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(Statement 1) x=9

when y is unknown, assuming even a positive value of y,

when y=1, x^2y=81, rem=1
when y=2, x^2y=6561, rem=1

We can see a pattern forming here, for all positive values of y, even powers of 9 will leave a remainder = 1, when divided by 10.
So, statement 1 is SUFFICIENT

(Statement 2) y=2
knowing just y without x is not sufficient for us to even find out the unit digit of the resulting value, statement 2 is thus INSUFFICIENT.


Answer: A
avatar
axmanX
avatar
Joined: 08 Jul 2018
Last visit: 16 Jun 2020
Posts: 23
Own Kudos:
20
Given Kudos: 43
Location: India
Concentration: General Management, Marketing
GPA: 4
Products:
My Reviews
Posts: 23
Kudos: 20
What is the remainder when x^2y is divided by 10? 28 Jul 2018, 16:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
axmanX
(Statement 1) x=9

when y is unknown, assuming even a positive value of y,

when y=1, x^2y=81, rem=1
when y=2, x^2y=6561, rem=1

Answer: A

you missed out y as fraction..

\(x^2y\) divided by 10 MEANS units digit of x^2y

1) x=9..
if y is integer, units digit will always be 1
if y is a fraction say 1/2, units digit will be 9
insuff

2) y = 2
will depend on x
x is 1, ans is 1
x is 2 ans is 6
insuff

combined
ans is 1
suff

C

NOTE - always work for integer and fraction and 0 unless specified

Makes sense. Thanks for correcting me!
avatar
devlin
avatar
Joined: 23 Aug 2017
Last visit: 11 Oct 2018
Posts: 19
Own Kudos:
4
Given Kudos: 5
Posts: 19
Kudos: 4
What is the remainder when x^2y is divided by 10? 31 Jul 2018, 06:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1:

The Pattern is:
When the exponent is odd the unit digit is 9, when it is even the unit digit is 1. As we don't know whether Y is an integer or even whether if Y > 0, then inssuficient.

Statement 2:
We need to know the value of X. Not Sufficient.

1) & 2) As we know now that Y is an integer greater than zero the remainder will be 1. Sufficient.

Posted from my mobile device
User avatar
satya2029
User avatar
Joined: 10 Dec 2017
Last visit: 09 Jul 2025
Posts: 231
Own Kudos:
241
Given Kudos: 136
Location: India
Posts: 231
Kudos: 241
What is the remainder when x^2y is divided by 10? 13 Jun 2020, 21:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
What is the remainder when \(x^{2y}\) is divided by 10?

(1) x=9
(2) y=2

Chetan's questions
Since odd power raised to 9 gives you 9 as unit digit while even power gives you 1 as unit digit.
here if y=1/2 as nothing is mentioned about y
9^1/10
Remainder is 9
while
9^2/10
Remainder is 1
Y alone does not decide here the unit digit of x^(2y)
Combining both the given conditions we can say that
X^2Y is 9^4
even power- 1 as unit digit
Remainder is 1
C:)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,365
Own Kudos:
1,010
Posts: 37,365
Kudos: 1,010
What is the remainder when x^2y is divided by 10? 03 Feb 2023, 10:05
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.
Moderator:
Bunuel
Math Expert
102612 posts