GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Aug 2019, 15:49

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.

Close

Request Expert Reply

Confirm Cancel

Is p^2 - 1 divisible by 12?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Current Student
avatar
B
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34
WE: Engineering (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Is p^2 - 1 divisible by 12?  [#permalink]

Show Tags

New post Updated on: 15 Aug 2014, 09:13
7
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:30) correct 33% (01:23) wrong based on 195 sessions

HideShow timer Statistics

Is p^2 - 1 divisible by 12?

(1) p > 3

(2) p is a prime number

Source: 4gmat

Originally posted by alphonsa on 15 Aug 2014, 08:13.
Last edited by Bunuel on 15 Aug 2014, 09:13, edited 1 time in total.
Edited the question
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57155
Re: Is p^2 - 1 divisible by 12?  [#permalink]

Show Tags

New post 15 Aug 2014, 09:23
2
4
Is p^2 - 1 divisible by 12?

(1) p > 3. This one is clearly insufficient: if p = 4, then the answer is NO but if p = 5, then the answer is YES. Not sufficient.

(2) p is a prime number. If p = 2, then the answer is NO but if p = 5, then the answer is YES. Not sufficient.

(1)+(2) Important property:
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.

So, according to the above, p can be expressed as \(p=6n+1\) or \(p=6n-1\). If \(p=6n+1\), then \(p^2 - 1 = 36n^2 +12n=12(3n^2+1)\) and if \(p=6n-1\), then \(p^2 - 1 = 36n^2 -12n=12(3n^2-1)\). In both cases p is a multiple of 12. Sufficient.

Answer: C.
_________________
General Discussion
Manager
Manager
User avatar
G
Joined: 13 Oct 2013
Posts: 135
Concentration: Strategy, Entrepreneurship
GMAT ToolKit User
Re: Is p^2 - 1 divisible by 12?  [#permalink]

Show Tags

New post 16 Aug 2014, 19:27
Hi Bunuel,
for P = 5 or 7 , p^2-1 is divisible by 12.
Should not answer be E?



Bunuel wrote:
Is p^2 - 1 divisible by 12?

(1) p > 3. This one is clearly insufficient: if p = 4, then the answer is NO but if p = 5, then the answer is YES. Not sufficient.

(2) p is a prime number. If p = 2, then the answer is NO but if p = 5, then the answer is YES. Not sufficient.

(1)+(2) Important property:
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.

So, according to the above, p can be expressed as \(p=6n+1\) or \(p=6n-1\). If \(p=6n+1\), then \(p^2 - 1 = 36n^2 +12n=12(3n^2+1)\) and if \(p=6n-1\), then \(p^2 - 1 = 36n^2 -12n=12(3n^2-1)\). In both cases p is a multiple of 12. Sufficient.

Answer: C.

_________________
---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way :)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57155
Re: Is p^2 - 1 divisible by 12?  [#permalink]

Show Tags

New post 17 Aug 2014, 04:05
sunita123 wrote:
Hi Bunuel,
for P = 5 or 7 , p^2-1 is divisible by 12.
Should not answer be E?



Bunuel wrote:
Is p^2 - 1 divisible by 12?

(1) p > 3. This one is clearly insufficient: if p = 4, then the answer is NO but if p = 5, then the answer is YES. Not sufficient.

(2) p is a prime number. If p = 2, then the answer is NO but if p = 5, then the answer is YES. Not sufficient.

(1)+(2) Important property:
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.

So, according to the above, p can be expressed as \(p=6n+1\) or \(p=6n-1\). If \(p=6n+1\), then \(p^2 - 1 = 36n^2 +12n=12(3n^2+1)\) and if \(p=6n-1\), then \(p^2 - 1 = 36n^2 -12n=12(3n^2-1)\). In both cases p is a multiple of 12. Sufficient.

Answer: C.


For any prime number p greater than 3, p^2 - 1 IS divisible by 12. So, taken together the statements are sufficient to get a definite YES answer to the question. Which means that the answer is C.
_________________
Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 158
GMAT ToolKit User
Re: Is p^2 - 1 divisible by 12?  [#permalink]

Show Tags

New post 17 Aug 2014, 16:24
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.


Again, I have never known the concept before. Thank you, Bunuel :-D :-D
_________________
.........................................................................
+1 Kudos please, if you like my post
Intern
Intern
avatar
Joined: 05 Sep 2014
Posts: 6
Is p^2 - 1 divisible by 12?  [#permalink]

Show Tags

New post 05 Oct 2014, 12:17
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.

I have a problem with highlighted part. How can we represent 5 or 7 in the forms 6n +1 or 6n +5. I think the above property holds good for n>=0. Can somebody clarify?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57155
Re: Is p^2 - 1 divisible by 12?  [#permalink]

Show Tags

New post 06 Oct 2014, 00:31
Intern
Intern
avatar
Joined: 05 Sep 2014
Posts: 6
Re: Is p^2 - 1 divisible by 12?  [#permalink]

Show Tags

New post 08 Oct 2014, 09:44
Thank you Bunnel for your prompt response! You are truly incredible!
VP
VP
avatar
G
Joined: 09 Mar 2018
Posts: 1001
Location: India
Is p^2 - 1 divisible by 12?  [#permalink]

Show Tags

New post 05 Jan 2019, 09:04
alphonsa wrote:
Is p^2 - 1 divisible by 12?

(1) p > 3

(2) p is a prime number

Source: 4gmat


\(p^2 - 1\)
can be written as (p-1) (p+1)

Statement 1 -> p=4,5,6
Case 1: 4, \(\frac{5*6}{12}\) , Question will be answered by a No

Case 2 : 5, \(\frac{4*6}{12}\), Question will be answered by a Yes

Statement 2-> p =2,5
Case 1: 2, \(\frac{1*3}{12}\), Question will be answered by a No

Case 2 : 5, \(\frac{4*6}{12}\), Question will be answered by a Yes

Combine, you will get a Yes if you take the case as p = 5, 7
Case 1 : 5, \(\frac{4*6}{12}\)

Case 2: 7, \(\frac{8*6}{12}\)

Correct Answer C
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
GMAT Club Bot
Is p^2 - 1 divisible by 12?   [#permalink] 05 Jan 2019, 09:04
Display posts from previous: Sort by

Is p^2 - 1 divisible by 12?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne