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:

Which of the following numbers is not prime ? [#permalink]
03 May 2012, 00:14

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

69% (01:54) correct
31% (01:09) wrong based on 224 sessions

Which of the following numbers is not prime? (Hint: avoid actually computing these numbers.)

A. 6!-1 B. 6!+21 C. 6!+41 D. 7!-1 E. 7!+11

Could please someone expalin the logic behind this ? Even though I picked the right answer while solving I am not pretty clear about the underlying concept?

Re: Which of the following numbers is not prime ? [#permalink]
03 May 2012, 00:21

1

This post received KUDOS

Expert's post

abhi47 wrote:

Which of the following numbers is not prime? (Hint: avoid actually computing these numbers.)

A. 6!-1 B. 6!+21 C. 6!+41 D. 7!-1 E. 7!+11

Could please someone expalin the logic behind this ? Even though I picked the right answer while solving I am not pretty clear about the underlying concept?

Thanks, Abhi

Notice that we can factor out 3 out of 6!+21 --> 6!+21=3*(2*4*5*6+7), which means that this number is not a prime.

Re: Which of the following numbers is not prime ? [#permalink]
03 May 2012, 00:36

Bunuel wrote:

abhi47 wrote:

Which of the following numbers is not prime? (Hint: avoid actually computing these numbers.)

A. 6!-1 B. 6!+21 C. 6!+41 D. 7!-1 E. 7!+11

Could please someone expalin the logic behind this ? Even though I picked the right answer while solving I am not pretty clear about the underlying concept?

Thanks, Abhi

Notice that we can factor out 3 out of 6!+21 --> 6!+21=3*(2*4*5*6+7), which means that this number is not a prime.

Answer: B.

@ Bunuel - what inference does 'factor out 3' make? can we say that the second part of the options (11,41) are prime so resultant could be a prime? but 1. could u pls explain?

Re: Which of the following numbers is not prime ? [#permalink]
03 May 2012, 08:38

3

This post received KUDOS

Expert's post

abhi47 wrote:

Which of the following numbers is not prime? (Hint: avoid actually computing these numbers.)

A. 6!-1 B. 6!+21 C. 6!+41 D. 7!-1 E. 7!+11

Could please someone expalin the logic behind this ? Even though I picked the right answer while solving I am not pretty clear about the underlying concept?

Thanks, Abhi

A prime number has only two factors - 1 and itself.

Without calculating, we cannot say whether 6!-1 or 6!+41 will be prime.

But, I can say that 6!+21 will not be prime. The reason is that 6!+21 = 3(1*2*4*5*6 + 7) (taking 3 common). This means that whatever, the value of 6!+21, it can be written as the product of two numbers: 3 and something else. Hence, this number, 6!+21, definitely has 3 as a factor and hence it cannot be prime. Since a PS question can have only one correct answer, we don't have to worry about the other options. We can say with certainty that they must be prime. _________________

Re: Which of the following numbers is not prime ? [#permalink]
12 Jun 2013, 14:26

Prime numbers are of the form 6n+1 or 6n-1. The first part of each of the terms contains a 6,and hence is a multiple of 6. We only need to factor out 6's from the 2nd part of each option. If you're left with a number greater than one, then that's the answer . In this case, that would be B.

Re: Which of the following numbers is not prime ? [#permalink]
12 Jun 2013, 14:43

1

This post received KUDOS

Expert's post

v1gnesh wrote:

Prime numbers are of the form 6n+1 or 6n-1. The first part of each of the terms contains a 6,and hence is a multiple of 6. We only need to factor out 6's from the 2nd part of each option. If you're left with a number greater than one, then that's the answer . In this case, that would be B.

Don't get your solution...

The property you are referring to is: 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. _________________

Re: Which of the following numbers is not prime ? [#permalink]
12 Jun 2013, 17:52

Bunuel wrote:

Don't get your solution...

The property you are referring to is: 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.

Thank you! Glad I can correct my understanding now rather than later.

Re: Which of the following numbers is not prime ? [#permalink]
17 Sep 2014, 11:19

I got it really fast 6! is not a prime, so in order to get a non-prime number, we have to add a non-prime number. 21 is not a prime number, therefore 6!+21 is not prime.

gmatclubot

Re: Which of the following numbers is not prime ?
[#permalink]
17 Sep 2014, 11:19

Hey, Last week I started a few new things in my life. That includes shifting from daily targets to weekly targets, 45 minutes of exercise including 15 minutes of yoga, making...

This week went in reviewing all the topics that I have covered in my previous study session. I reviewed all the notes that I have made and started reviewing the Quant...

I started running as a cross country team member since highshcool and what’s really awesome about running is that...you never get bored of it! I participated in...