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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Is the two digit positive integer P a prime number? [#permalink]
21 Oct 2010, 16:52

1

This post received KUDOS

Expert's post

3

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.

Re: Is the two digit positive integer P a prime number? [#permalink]
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.

Re: Is the two digit positive integer P a prime number? [#permalink]
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 !

Re: Is the two digit positive integer P a prime number? [#permalink]
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. _________________

Is the two digit positive integer P a prime number? [#permalink]
06 Aug 2015, 12:41

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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. D. EACH statement ALONE is sufficient to answer the question asked. E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Re: Is the two digit positive integer P a prime number? [#permalink]
06 Aug 2015, 12:56

Tornikea 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. D. EACH statement ALONE is sufficient to answer the question asked. E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Please search for a question before re-posting a question that has already been discussed. Refer above for the solution. _________________

Hey, everyone. After a hectic orientation and a weeklong course, Managing Groups and Teams, I have finally settled into the core curriculum for Fall 1, and have thus found...

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

After I was accepted to Oxford I had an amazing opportunity to visit and meet a few fellow admitted students. We sat through a mock lecture, toured the business...