Last visit was: 23 Apr 2026, 18:39 It is currently 23 Apr 2026, 18:39
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
Back to Forum
Create Topic
User avatar
amanvermagmat
User avatar
Retired Moderator
Joined: 22 Aug 2013
Last visit: 28 Mar 2025
Posts: 1,142
Own Kudos:
2,973
 [4]
Given Kudos: 480
Location: India
Posts: 1,142
Kudos: 2,973
 [4]
What is the remainder when y^2 is divided by 6? (1) y is a prime numb 02 Apr 2018, 04:54
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

40% (02:14) correct 60% (01:51) wrong based on 87 sessions

History

Date
Time
Result
Not Attempted Yet
What is the remainder when y^2 is divided by 6?

(1) y is a prime number greater than 10.

(2) y is a positive odd number which is NOT divisible by 3.
ShowHide Answer
Official Answer
D
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 23 Apr 2026
Posts: 1,922
Own Kudos:
6,856
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,922
Kudos: 6,856
What is the remainder when y^2 is divided by 6? (1) y is a prime numb Updated on: 02 Apr 2018, 17:53
Originally posted by GMATBusters on 02 Apr 2018, 06:28.
Last edited by GMATBusters on 02 Apr 2018, 17:53, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1 : y is a prime number greater than 10.
Any prime no greater than 3 can be represented by 6n+1 or 6n-1
Now \(y ^2 = (6n+1)^2 or (6n-1)^2\)
\(y^2 = (36n^2+12n+1) or (36n^2-12n+1)\)
Hence remainder when y ^2 divisible by 6 = 1
Sufficient.

Statement 2: y is a positive odd number which is NOT divisible by 3.
y can be 7 : y ^2 = 49. remainder when divided by 6 =1
y can be 11: y^2 = 121, remainder when divided by 6 = 1
It will always be 1.
sufficient.

Answer D
User avatar
kunalcvrce
User avatar
Joined: 05 Feb 2016
Last visit: 09 Apr 2025
Posts: 131
Own Kudos:
135
Given Kudos: 72
Location: India
Concentration: General Management, Marketing
WE:Information Technology (Computer Software)
Posts: 131
Kudos: 135
What is the remainder when y^2 is divided by 6? (1) y is a prime numb Updated on: 02 Apr 2018, 20:06
Originally posted by kunalcvrce on 02 Apr 2018, 08:44.
Last edited by kunalcvrce on 02 Apr 2018, 20:06, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
amanvermagmat
What is the remainder when y^2 is divided by 6?

(1) y is a prime number greater than 10.

(2) y is a positive odd number which is NOT divisible by 3.
Show more


Statement 1 : y is a prime number greater than 10.
Any prime no greater than 3 can be represented by 6n+1 or 6n-1

By remainder theorem the remainder of y ^2 will product of individual remainders.
for 6n+1 =rem(1) when divided by 6 so ,actual remainder for y ^2 =1*1=1
6n-1 = rem(-1) when divided by 6 so ,actual remainder for y ^2=-1*-1=1
Hence remainder when y ^2 divisible by 6 = 1
Sufficient.

Statement 2: y is a positive odd number which is NOT divisible by 3.
y can be 7 : remainder when divided by 6 =1
y can be 11: when divided by 6 = 1
sufficient.

Answer D
User avatar
aserghe1
User avatar
Joined: 30 Mar 2017
Last visit: 26 Oct 2021
Posts: 83
Own Kudos:
174
 [2]
Given Kudos: 53
GMAT 1: 200 Q1 V1
Products:
My Reviews
GMAT 1: 200 Q1 V1
Posts: 83
Kudos: 174
 [2]
What is the remainder when y^2 is divided by 6? (1) y is a prime numb 02 Apr 2018, 15:56
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Statement 2 is also sufficient

Given: y is a positive odd number which is NOT divisible by 3.
so y=3k+1 where k is even, or y=3k+2 where k is odd.

Case 1 (y=3k+1 where k is even)
\(y^2=(3k+1)^2=9k^2+6k+1\)
since k is even, we can write k=2a where a is an integer, and substitute
\(y^2=9k^2+6k+1=9(2a)^2+6(2a)+1=36a^2+12a+1\)
So remainder = 1 when divided by 6.

Case 2 (y=3k+2 where k is odd)
\(y^2=(3k+2)^2=9k^2+12k+4\)
since k is odd, we can write k=2b+1 where b is an integer, and substitute
\(y^2=9k^2+12k+4=9(2b+1)^2+12(2b+1)+4=9(4b^2+4b+1)+24b+12+4=36b^2+60b+25\)
So remainder = 1 when divided by 6.

Sufficient

Or you could try some numbers that meet the condition, e.g.
1^2=1; remainder=1 when div by 6
5^2=25; remainder=1 when div by 6
7^2=49; remainder=1 when div by 6

I dont know if this method is reliable though.

Answer: D
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 23 Apr 2026
Posts: 1,922
Own Kudos:
6,856
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,922
Kudos: 6,856
What is the remainder when y^2 is divided by 6? (1) y is a prime numb 02 Apr 2018, 17:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hii
You are right, answer should be D.

I forgot that question is asking for remainser when y^2 is divided by 6, not when y is divided by 6.
Thanks for pointng out.

Kudos to you.

aserghe1
Statement 2 is also sufficient

Given: y is a positive odd number which is NOT divisible by 3.
so y=3k+1 where k is even, or y=3k+2 where k is odd.

Case 1 (y=3k+1 where k is even)
\(y^2=(3k+1)^2=9k^2+6k+1\)
since k is even, we can write k=2a where a is an integer, and substitute
\(y^2=9k^2+6k+1=9(2a)^2+6(2a)+1=36a^2+12a+1\)
So remainder = 1 when divided by 6.

Case 2 (y=3k+2 where k is odd)
\(y^2=(3k+2)^2=9k^2+12k+4\)
since k is odd, we can write k=2b+1 where b is an integer, and substitute
\(y^2=9k^2+12k+4=9(2b+1)^2+12(2b+1)+4=9(4b^2+4b+1)+24b+12+4=36b^2+60b+25\)
So remainder = 1 when divided by 6.

Sufficient

Or you could try some numbers that meet the condition, e.g.
1^2=1; remainder=1 when div by 6
5^2=25; remainder=1 when div by 6
7^2=49; remainder=1 when div by 6

I dont know if this method is reliable though.

Answer: D
Show more

Posted from my mobile device
avatar
MohammedJunaid
avatar
Joined: 15 Apr 2014
Last visit: 09 May 2024
Posts: 1
Own Kudos:
5
Posts: 1
Kudos: 5
What is the remainder when y^2 is divided by 6? (1) y is a prime numb 02 Apr 2018, 23:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi,

Question: Remainder when y^2 divided by 6 ?

Any integer when divided by 6 leaves remainders as 0,1,2,3,4 and 5.

Statement I is sufficient:

Prime number greater than 10.

Yes there is a rule which says, when any prime number greater than 3 can be expressed as 6n+1 or 6n+5.

So according to the rule,

y=6n+1 or y = 6n+5

y^2 = 36n + 12n + 1

or

y^2 = 36n + 60n + 25.

So, both expression when divided by 6, leaves the remainder 1.

Even if you don’t remember this rule(this rule has been discussed in Official GMAT guide), its okay, you just need to try out some values and check out the pattern of y^2. Different pattern then
its not sufficient, if it gives you same result every time then it is sufficient.

Let’s say,

y = 11 , 13, 17, 19

y^2 = 121, 169, 289, 361.

All leaves remainder 1 when divided by 6(Divisibility rule for 6 is it should be divisible by both 3 and 2). So sufficient.

Statement II is sufficient:

y = 1, 5, 7, 11, 13, 17,..

y^2 = 1, 25, 49, 121, 169, 289..

Again, all leaves remainder 1 when divided by 6.

So, each alone are sufficient. So answer is D.

Trying out numbers would be the ideal approach for these types of questions.

Hope this helps.
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 23 Apr 2026
Posts: 6,976
Own Kudos:
16,908
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: 6,976
Kudos: 16,908
What is the remainder when y^2 is divided by 6? (1) y is a prime numb 03 Apr 2018, 02:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
amanvermagmat
What is the remainder when y^2 is divided by 6?

(1) y is a prime number greater than 10.

(2) y is a positive odd number which is NOT divisible by 3.
Show more

A point for readers of this thread and specially for the ones who face challenge in QUANT Section

While it's alright to use that Prime number greater than 3 are (6k+1) or (6k-1) form but ONLY IF YOU ALREADY KNOW.

THIS PROPERTY OF PRIME NUMBER IS UN-NECESSARY FOR ANY GMAT RELATED QUESTION

Question : remainder when y^2 is divided by 6?

Statement 1: y is a prime number greater than 10
i.e. y maybe 11, 13, 17. 19, 23 ... etc

Remainder (y^2/6) = R(121/6) or R(169/6) or R(289/6) or ... = 1 always hence . [Check for 3 consecutive cases like shown here]

SUFFICIENT

Statement 2: y is a positive odd number which is NOT divisible by 3

i.e. y may be 5, 7, 11, 13, .. etc
y^2 may be 25, 49, 121, 169 etc
remainder are 1 hence

SUFFICIENT

Answer: option D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
1,117
Posts: 38,964
Kudos: 1,117
What is the remainder when y^2 is divided by 6? (1) y is a prime numb 03 Oct 2024, 10:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
109785 posts
kingbucky
498 posts
Gmat860sanskar
212 posts