NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 16:01 It is currently 23 Apr 2024, 16:01
Decision Tracker
My Rewards
New posts
New comers' posts

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

If n is a prime number greater than 3, what is the remainder when n^2

SORT BY:
Date
Kudos
Tags:
Difficulty: Sub 505 Levelx   Remaindersx                           
Find Similar Topics 
Show Tags
Hide Tags
avatar
chonepiece
Intern
Intern
Joined: 10 Aug 2011
Posts: 1
Own Kudos [?]: 50 [50]
Given Kudos: 0
Send PM
If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   Updated on: 13 Aug 2019, 02:38
9
Kudos
41
Bookmarks
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

96% (00:44) correct 4% (01:06) wrong based on 3676 sessions
Hide Show timer Statistics
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
ShowHide Answer
Official Answer
B

Originally posted by chonepiece on 28 Oct 2011, 05:13.
Last edited by Bunuel on 13 Aug 2019, 02:38, edited 3 times in total.
Edited the question
Most Helpful Reply
avatar
koolgmat
Intern
Intern
Joined: 16 May 2013
Posts: 15
Own Kudos [?]: 166 [89]
Given Kudos: 13
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   27 Jun 2013, 10:00
58
Kudos
30
Bookmarks
Bunuel wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

Practice Questions
Question: 26
Page: 155
Difficulty: 600


All Prime numbers greater than 3 and upto 1000000000000000 can be expressed in the form of 6k+1 or 6k-1 , where k is a not negative integer.

Say N = 6k+1
N^2 = (6k+1)^2 = 36K^2 + 12K + 1 = 12(3K^2 + K) +1

Since 12(3K^2+K) is exactly divisible by 12 , therefore N^2 when divided by 12 leaves a remainder as 1.

Same can be proved for N = 6K -1
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618586 [38]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   26 Aug 2012, 02:56
17
Kudos
20
Bookmarks
Expert Reply
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

There are several algebraic ways to solve this question, but the easiest way is as follows: since we cannot have two correct answers just pick a prime greater than 3, square it and see what would be the remainder upon division of it by 12.

n=5 --> n^2=25 --> remainder upon division 25 by 12 is 1.

Answer: B.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618586 [22]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   01 Nov 2012, 05:54
12
Kudos
10
Bookmarks
Expert Reply
sachindia wrote:
VeritasPrepKarishma wrote:
sdas wrote:
all i did was pick numbers and try...got remainder as 1 always. so B. anything wrong in my approach pls advice


No. Nothing wrong. Just that you don't need to try many numbers. There will only be one answer to a PS question. So all you need to do is try any one number greater than 3. Whatever you get, that will be the answer in every case.


I wonder why every prime no greater than 3 when squared and divided by 4 results in the remainder of 1 :shock:


Any prime number \(p\) greater than 3 could be expressed as \(p=6n+1\) or \(p=6n+5\) (\(p=6n-1\)), where \(n\) is an integer >1.

That's because any prime number \(p\) greater than 3 when divided by 6 can only give remainder of 1 or 5 (remainder can not be 2 or 4 as in this case \(p\) would be even and remainder can not be 3 as in this case \(p\) would be divisible by 3).

But:
Note that, not all number which yield a remainder of 1 or 5 upon division by 6 are primes, so vise-versa of above property is not correct. For example 25 (for \(n=4\)) yields a remainder of 1 upon division by 6 and it's not a prime number.

Now, if a prime is of the form \(p=6n+1\), then \(p^2=36n^2+12n+1=12(3n^2+n)+1\) and if a prime is of the form \(p=6n-1\), then \(p^2=36n^2-12n+1=12(3n^2-n)+1\). Both yield the remainder of 1 when divided by 12.

Hope it's clear.
General Discussion
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64882 [7]
Given Kudos: 426
Location: Pune, India
Send PM
If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   Updated on: 11 Oct 2022, 00:51
3
Kudos
4
Bookmarks
Expert Reply
chonepiece wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?
A. 0
B. 1
C. 2
D. 3
E. 5

it's a simple quesiton, but the solutuion is inspiring.

Show SpoilerSolution
n^2-1=(n-1)(n+1)
since (n-1) and (n+1) are consecutive even numbers,one of them can be divided by 2, another one can be divided by 4;
and because n can not be divided by 3, so one of (n-1) and (n+1) can be divided by 3.
So (n-1)(n+1)=n^2-1 is divisible by 24, then the remainder of n^2 divided by 24 is 1.


Please check my signature for the link to the relevant blog posts.
...and of course, the most efficient solution would be what Bunuel suggested - Pick a prime number > 3 and check for it!

Originally posted by KarishmaB on 10 Feb 2012, 02:33.
Last edited by KarishmaB on 11 Oct 2022, 00:51, edited 1 time in total.
User avatar
sdas
Senior Manager
Senior Manager
Joined: 23 Mar 2011
Posts: 365
Own Kudos [?]: 637 [2]
Given Kudos: 59
Location: India
Schools: Rotman '16 Ivey '15 Queens'16 INSEAD Jan '16
GPA: 2.5
WE:Operations (Hospitality and Tourism)
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   10 Feb 2012, 02:47
1
Kudos
all i did was pick numbers and try...got remainder as 1 always. so B. anything wrong in my approach pls advice
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64882 [3]
Given Kudos: 426
Location: Pune, India
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   10 Feb 2012, 02:54
2
Kudos
1
Bookmarks
Expert Reply
sdas wrote:
all i did was pick numbers and try...got remainder as 1 always. so B. anything wrong in my approach pls advice


No. Nothing wrong. Just that you don't need to try many numbers. There will only be one answer to a PS question. So all you need to do is try any one number greater than 3. Whatever you get, that will be the answer in every case.
User avatar
Sachin9
Senior Manager
Senior Manager
Joined: 22 Jul 2012
Status:Gonna rock this time!!!
Posts: 356
Own Kudos [?]: 166 [1]
Given Kudos: 562
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE:Information Technology (Computer Software)
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   01 Nov 2012, 03:13
1
Kudos
VeritasPrepKarishma wrote:
sdas wrote:
all i did was pick numbers and try...got remainder as 1 always. so B. anything wrong in my approach pls advice


No. Nothing wrong. Just that you don't need to try many numbers. There will only be one answer to a PS question. So all you need to do is try any one number greater than 3. Whatever you get, that will be the answer in every case.


I wonder why every prime no greater than 3 when squared and divided by 4 results in the remainder of 1 :shock:
avatar
pavan2185
Manager
Manager
Joined: 15 Apr 2013
Posts: 63
Own Kudos [?]: 748 [0]
Given Kudos: 61
Location: India
Concentration: Finance, General Management
Schools: ISB '15
WE:Account Management (Other)
Send PM
GMAT ToolKit User
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   02 Jul 2013, 10:16
All the prime numbers >2 end with 1,3,5,7. Since the question stem says Primes >3, we need not check those ending with 1 & 3. so pick any numbers ending with 5&7 , you will get the same remainder.
User avatar
B
mau5
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 485
Own Kudos [?]: 3092 [3]
Given Kudos: 141
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   02 Jul 2013, 10:41
2
Kudos
1
Bookmarks
pavan2185 wrote:
All the prime numbers >2 end with 1,3,5,7.


No prime no can ever end in 5, except 5.


Since the question stem says Primes >3, we need not check those ending with 1 & 3.

11,13 are primes, which are greater than 3 and end with 1 and 3 respectively.

Moreover,the question asks for the remainder when \(n^2\) is divided by 12, not n.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618586 [2]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   02 Jul 2013, 10:51
2
Kudos
Expert Reply
mau5 wrote:
pavan2185 wrote:
All the prime numbers >2 end with 1,3,5,7.


No prime no can ever end in 5, except 5.


Since the question stem says Primes >3, we need not check those ending with 1 & 3.

11,13 are primes, which are greater than 3 and end with 1 and 3 respectively.

Moreover,the question asks for the remainder when \(n^2\) is divided by 12, not n.


We can simply check for the first prime which is greater than 3, so for 5: n=5 --> n^2=25 --> remainder upon division 25 by 12 is 1.

Also, primes greater than 5 can have the units digit of 1, 3, 7, OR 9.
User avatar
RustyR
Manager
Manager
Joined: 11 Sep 2012
Posts: 81
Own Kudos [?]: 36 [0]
Given Kudos: 9
Schools: Darden '16 (A$) Tuck '16 (M) Ross '16 (A) Johnson '16 (A)
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   25 Dec 2013, 11:39
koolgmat wrote:
Bunuel wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

Practice Questions
Question: 26
Page: 155
Difficulty: 600


All Prime numbers greater than 3 and upto 1000000000000000 can be expressed in the form of 6k+1 or 6k-1 , where k is a not negative integer.

Say N = 6k+1
N^2 = (6k+1)^2 = 36K^2 + 12K + 1 = 12(3K^2 + K) +1

Since 12(3K^2+K) is exactly divisible by 12 , therefore N^2 when divided by 12 leaves a remainder as 1.

Same can be proved for N = 6K -1


How do we know that the prime number in questions is not larger than 10^15?

So that we know how to, how do we solve this problem algebraically?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618586 [4]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   26 Dec 2013, 03:39
4
Bookmarks
Expert Reply
bschoolaspirant9 wrote:
koolgmat wrote:
Bunuel wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

Practice Questions
Question: 26
Page: 155
Difficulty: 600


All Prime numbers greater than 3 and upto 1000000000000000 can be expressed in the form of 6k+1 or 6k-1 , where k is a not negative integer.

Say N = 6k+1
N^2 = (6k+1)^2 = 36K^2 + 12K + 1 = 12(3K^2 + K) +1

Since 12(3K^2+K) is exactly divisible by 12 , therefore N^2 when divided by 12 leaves a remainder as 1.

Same can be proved for N = 6K -1


How do we know that the prime number in questions is not larger than 10^15?

So that we know how to, how do we solve this problem algebraically?


n^2 can be greater than 10^15 and the property would still hold true. koolgmat incorrectly limited the upper limit to 10^15.

The property koolgmat is referring to is: ANY prime number \(p\) greater than 3 can be expressed as \(p=6n+1\) or \(p=6n+5\) (\(p=6n-1\)), where \(n\) is an integer >1.

That's because any prime number \(p\) greater than 3 when divided by 6 can only give remainder of 1 or 5 (remainder can not be 2 or 4 as in this case \(p\) would be even and remainder can not be 3 as in this case \(p\) would be divisible by 3).

But:
Note that, not all number which yield a remainder of 1 or 5 upon division by 6 are primes, so vise-versa of above property is not correct. For example 25 (for \(n=4\)) yields a remainder of 1 upon division by 6 and it's not a prime number.

Hope it's clear.

P.S. Similar question to practice: if-n-4p-where-p-is-a-prime-number-greater-than-2-how-man-144781.html
avatar
B
OptimusPrepJanielle
SVP
SVP
Joined: 06 Nov 2014
Posts: 1798
Own Kudos [?]: 1367 [0]
Given Kudos: 23
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   31 Mar 2015, 12:07
Expert Reply
Bunuel wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

Practice Questions
Question: 26
Page: 155
Difficulty: 600


There are infinite prime numbers greater than 3.
So one this is sure that all prime numbers (greater than 3) when squared and then divided by 12 will have the same remainder.
So let us assume that the prime number is 5.
So, 5^2 = 25 when divided by 12 gives 1 as remainder.
Hence option (B).

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18753
Own Kudos [?]: 22041 [2]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   04 May 2016, 09:52
2
Bookmarks
Expert Reply
chonepiece wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?

A. 0
B. 1
C. 2
D. 3
E. 5



Solution:

We see that n can be ANY PRIME NUMBER GREATER THAN 3. Let’s choose the smallest prime number greater than 3 and substitute it for n; that number is 5.

We know that 5 squared is 25, so we now divide 25 by 12:

25/12 = 2, Remainder 1.

If you are not convinced by trying just one prime number, try another one. Let’s try 7. We know that 7 squared equals 49, so we now divide 49 by 12:

49/12 = 4, Remainder 1.

It turns out that in this problem it doesn’t matter which prime number (greater than 3) we choose. The remainder will always be 1 when its square is divided by 12.

Answer B.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29893 [1]
Given Kudos: 799
Location: Canada
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   22 Apr 2020, 09:21
1
Kudos
Expert Reply
Top Contributor
chonepiece wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5


A nice fast approach is to TEST a possible value of n.
Since n must be a prime number that's greater than 3, let's TEST n = 5

If n = 5, then n² = 5² = 25, and when we divide 25 by 12, we get 2 with REMAINDER 1

Answer: B

Cheers,
Brent
User avatar
P
MHIKER
Director
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 972
Own Kudos [?]: 4927 [0]
Given Kudos: 690
Concentration: Accounting
Send PM
If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   07 Dec 2020, 06:24
Top Contributor
chonepiece wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5


\(n=5, n^2=25\)

\(\frac{25}{12}= 2 \ Remainder \ is 1\)

The answer is B
User avatar
P
100mitra
Director
Director
Joined: 29 Apr 2019
Status:Learning
Posts: 751
Own Kudos [?]: 583 [0]
Given Kudos: 49
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   19 Sep 2021, 03:10
Special thankful notes from GMAT Club Quants book
Any prime number greater than 3 could be expressed as (p=6n+1) or p(=6n-1),
where n is an integer >1, reminder will be 1

Answer Option : B (1)
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1777
Own Kudos [?]: 2094 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   19 Oct 2022, 12:03
Expert Reply
Top Contributor
Given that n is a prime number greater than 3 and we need to find what is the remainder when \(n^2\) is divided by 12

Lets take a prime number greater than 3
=> n = 5

(Watch this video to know about Prime Numbers)

\(n^2\) = \(5^2\) = 25

\(n^2\) i.e. 25 when divided by 12 will give 1 remainder

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32627
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink] New post   21 Oct 2023, 16:34
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.
GMAT Club Bot
gmatclubot
Re: If n is a prime number greater than 3, what is the remainder when n^2 [#permalink]
21 Oct 2023, 16:34
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions