Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Oct 2014, 02:31

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is the two digit positive integer P a prime number?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
5 KUDOS received
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2794
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 182

Kudos [?]: 987 [5] , given: 235

Reviews Badge
Is the two digit positive integer P a prime number? [#permalink] New post 21 Oct 2010, 16:01
5
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

40% (02:08) correct 60% (01:36) wrong based on 41 sessions
Is the two digit positive integer P a prime number?

(1) P + 2 and P – 2 are prime.
(2) P – 4 and P + 4 are prime.
[Reveal] Spoiler: OA

_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html


Last edited by Bunuel on 14 Sep 2014, 16:29, edited 1 time in total.
Edited the question and added the OA.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23393
Followers: 3607

Kudos [?]: 28814 [1] , given: 2852

Re: Is the two digit positive integer P a prime number? [#permalink] New post 21 Oct 2010, 16:52
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
gurpreetsingh wrote:
Is the two digit positive integer P a prime number?

1) P + 2 and P – 2 are prime.
2) P – 4 and P + 4 are prime.

I will post the solution and the explanation later.


Good question, +1.

Note that P is the two digit integer .

(1) P + 2 and P – 2 are prime --> out of every 3 consecutive integers one must be divisible by 3 --> consider 5 consecutive integers: {P-2}{P-1}{P}{P+1}{P+2}. Now, P-2 and P+2 are not divisible by 3 as they are primes, P+1 and P-1 are 3 apart from P-2 and P+2 respectively and thus they are also not divisible by 3, which means that P must be divisible by 3 and as it's TWO digit integer it can not be a prime. Sufficient.

(2) P – 4 and P + 4 are prime --> the same here: {P-1}{P}{P+1}. P-1 and P+1 are 3 apart from P-4 and P+4 respectively and thus can not be divisible by 3, which means that P must be divisible by 3 and as it's TWO digit integer it can not be a prime. Sufficient.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2794
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 182

Kudos [?]: 987 [0], given: 235

Reviews Badge
Re: Is the two digit positive integer P a prime number? [#permalink] New post 21 Oct 2010, 17:49
Yes Bunuel, Its a very good question. That's why I thought I should share it here.

The only catch was the existence of two digit number. Since you have posted the solution. I will post mine strategy.

All the numbers can be represented as 3k,3k+1, 3k+2

Statement 1: For P+2 and P-2 to be prime the number can not be of the form 3k+1 and 3k+2.
=> P = 3k = not prime if k is not equal to 1
Since two digit number is given => 3k is not a prime number.

Statement 2: using the same strategy. P is not a prime number.

Hence D.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Manager
User avatar
Joined: 19 Feb 2009
Posts: 58
Schools: INSEAD,Nanyang Business school, CBS,
Followers: 2

Kudos [?]: 25 [0], given: 8

Re: Is the two digit positive integer P a prime number? [#permalink] New post 22 Oct 2010, 12:09
I solved this by different method,

1) P + 2 and P – 2 are prime.
--> if You can list out all two digit Prime Numbers, you will get P=15 ONLY for which P+2 & P-2 are primes.
since 15 is not prime, Sufficient

2) P – 4 and P + 4 are prime.
--> Again, if You can list out all two digit Prime Numbers, you will get P=15 ONLY for which P+4 & P-4 are primes.
since 15 is not prime, Sufficient

hence D.

though the answer is correct by this method, I feel Bunuel's Method was more proper !! :)
_________________

Working without expecting fruit helps in mastering the art of doing fault-free action !

Manager
Manager
User avatar
Joined: 19 Feb 2009
Posts: 58
Schools: INSEAD,Nanyang Business school, CBS,
Followers: 2

Kudos [?]: 25 [0], given: 8

Re: Is the two digit positive integer P a prime number? [#permalink] New post 22 Oct 2010, 21:53
Ohh yes... I missed many pairs... :o
gurpreetsingh , Thanks for the correction
_________________

Working without expecting fruit helps in mastering the art of doing fault-free action !

CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2831
Followers: 206

Kudos [?]: 42 [0], given: 0

Premium Member
Re: Is the two digit positive integer P a prime number? [#permalink] New post 14 Sep 2014, 08:30
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Is the two digit positive integer P a prime number?   [#permalink] 14 Sep 2014, 08:30
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Is the positive integer P a prime number? alphonsa 4 18 Aug 2014, 06:59
9 Experts publish their posts in the topic If p is a positive integer, is p a prime number? Bunuel 8 06 Jun 2014, 05:29
1 Experts publish their posts in the topic Is the two-digit prime number p equal to 17? BN1989 1 29 Feb 2012, 11:15
The number A is a two-digit positive integer; the number B 386390 0 22 Jul 2011, 09:09
Experts publish their posts in the topic If the two-digit integer P and Q are positive and have the lumone 4 27 Nov 2007, 07:23
Display posts from previous: Sort by

Is the two digit positive integer P a prime number?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.