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

 It is currently 18 Sep 2019, 10:57 ### 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

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. ### Request Expert Reply # Which of the following numbers is not prime ?

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

### Hide Tags

Manager  Joined: 17 Sep 2011
Posts: 126
Which of the following numbers is not prime ?  [#permalink]

### Show Tags

3
13 00:00

Difficulty:   35% (medium)

Question Stats: 67% (01:21) correct 33% (01:32) wrong based on 442 sessions

### HideShow timer Statistics

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

_________________
_________________
Giving +1 kudos is a better way of saying 'Thank You'.

Originally posted by abhi47 on 03 May 2012, 01:14.
Last edited by Bunuel on 03 May 2012, 01:19, edited 1 time in total.
Edited the question
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9637
Location: Pune, India
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

9
3
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.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 58092
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

3
4
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.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58092
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

1
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.
_________________
Senior Manager  Joined: 20 Aug 2015
Posts: 388
Location: India
GMAT 1: 760 Q50 V44 Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

1
IgnacioDeLoyola wrote:
Not sure if my logic is correct, but the way I figured this out was:

Rule: We know that all primes above 3 are in the form of either 6n-1 or 6n+1.

So:

A. 6!-1 -- Here we have 6*5*4,etc -1 (thus, in the form of 6n-1)
B. 6!+21 -- Here we have 6*5*4,etc + 7*3 -> This could be the answer as 21 isn't a prime number
C. 6!+41 -- Here we have 6*5*4,etc + prime number
D. 7!-1 -- Here we have 7*6*5*4,etc - 1 (thus, in the form of 6n-1)
E. 7!+11 -- Here we have 7*6*5*4,etc + prime number

Hi IgnacioDeLoyola,

The relation that you wrote is correct, but its reversal is not true. (you are assuming this in options A and D)
All prime numbers are of the form 6n+/- 1 but all numbers of the form 6n+/- 1 are not prime
Example: 7 = 6(1)+1 - Prime
25 = 6(4)+1 - Not Prime

Also, it is not necessary that any number when added to a prime number will be prime (which I feel you are assuming in options C and E)
Example: 7 (prime) +3 (prime) = 10 (not prime)

You should rely on finding the factors if you have to identify that a number is prime or not.
Manager  Joined: 02 Jun 2011
Posts: 115
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

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.

@ 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?
Intern  Joined: 25 Jun 2012
Posts: 29
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

The added or subtracted terms, all but one of them, is a prime number itself, that should be a sort of red flag.
Math Expert V
Joined: 02 Sep 2009
Posts: 58092
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Number Properties: math-number-theory-88376.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

_________________
Intern  Joined: 26 Mar 2013
Posts: 11
Location: United States
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

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.
Intern  Joined: 26 Mar 2013
Posts: 11
Location: United States
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

1
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.
Senior Manager  Joined: 20 Aug 2015
Posts: 388
Location: India
GMAT 1: 760 Q50 V44 Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

A prime number can have only two factors:1 and itself.
If we are able to prove that a number is divisible by any other number too, then we can say that the number is contention is not prime.

In this particular question, checking by options we can certainly say that 6! +21 = 3(6*5*4*2*1 + 7)
Hence 6! +21 is divisible by 3 and thus not a prime number
Intern  Joined: 22 Sep 2015
Posts: 5
Which of the following numbers is not prime ?  [#permalink]

### Show Tags

1
Not sure if my logic is correct, but the way I figured this out was:

Rule: We know that all primes above 3 are in the form of either 6n-1 or 6n+1.

So:

A. 6!-1 -- Here we have 6*5*4,etc -1 (thus, in the form of 6n-1)
B. 6!+21 -- Here we have 6*5*4,etc + 7*3 -> This could be the answer as 21 isn't a prime number
C. 6!+41 -- Here we have 6*5*4,etc + prime number
D. 7!-1 -- Here we have 7*6*5*4,etc - 1 (thus, in the form of 6n-1)
E. 7!+11 -- Here we have 7*6*5*4,etc + prime number

Current Student D
Joined: 12 Aug 2015
Posts: 2594
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

Primes cannot be written as a product of two numbers
Smash B
Stone Cold
_________________
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4705
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Which of the following numbers is not prime ?  [#permalink]

### Show Tags

stonecold wrote:
Primes cannot be written as a product of two numbers
Smash B
Stone Cold

Nothing just respect for you 6! + 21 = (6 x 5 x 4 x 3 x 2 x 1 ) + ( 3 x 7 )

Try to divide the number by 3 it is divisible.....

PS : Good going Austin Bro , keep it up !!
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager  S
Joined: 27 Aug 2016
Posts: 88
Location: India
Schools: HEC Montreal '21
GMAT 1: 670 Q47 V37 GPA: 3
WE: Engineering (Energy and Utilities)
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

mvictor wrote:
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.

Don't get ur solution:
Are we trying to say that adding two prime numbers will give a prime number?
Director  G
Joined: 02 Sep 2016
Posts: 653
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

A prime no. will have only two factors 1 and itself.

Adding prime nos. can give a prime (2+3=5) or a composite no. (3+5=8) (composite no. means any number which is not prime as it has prime factors>2 i.e. it is composed of other prime factors such as 12= 2^2*3).

Back to the question:

Only 6! +21 can be written as a product of more than 2 nos. including 1.

1*2*3*4*5*6 + (3*7)
=3(1*2*4*5*6+ 7)

Thus its not prime.
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Non-Human User Joined: 09 Sep 2013
Posts: 12370
Re: Which of the following numbers is not prime ?  [#permalink]

### Show Tags

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.
_________________ Re: Which of the following numbers is not prime ?   [#permalink] 10 Aug 2019, 17:48
Display posts from previous: Sort by

# Which of the following numbers is not prime ?

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

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