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

It is currently 30 May 2016, 13:32
GMAT Club Tests

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

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

1 KUDOS received
Manager
Manager
avatar
Joined: 17 Sep 2011
Posts: 209
Followers: 0

Kudos [?]: 82 [1] , given: 8

Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 03 May 2012, 01:14
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (02:01) correct 31% (01:09) wrong based on 307 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
[Reveal] Spoiler: OA

_________________

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


Last edited by Bunuel on 03 May 2012, 01:19, edited 1 time in total.
Edited the question
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33075
Followers: 5777

Kudos [?]: 70917 [1] , given: 9857

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 03 May 2012, 01:21
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.

Answer: B.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 02 Jun 2011
Posts: 159
Followers: 1

Kudos [?]: 63 [0], given: 11

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 03 May 2012, 01:36
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?
Expert Post
5 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6584
Location: Pune, India
Followers: 1795

Kudos [?]: 10813 [5] , given: 212

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 03 May 2012, 09:38
5
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
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
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 25 Jun 2012
Posts: 36
Followers: 0

Kudos [?]: 28 [0], given: 4

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 27 Nov 2012, 17:23
The added or subtracted terms, all but one of them, is a prime number itself, that should be a sort of red flag.
Manager
Manager
avatar
Joined: 11 Aug 2012
Posts: 128
Schools: HBS '16, Stanford '16
Followers: 1

Kudos [?]: 72 [0], given: 16

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 27 Nov 2012, 17:40
+1 B

6! is multiple of 21 (= 3 * 7)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33075
Followers: 5777

Kudos [?]: 70917 [0], given: 9857

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 12 Jun 2013, 05:25
Expert's post
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

_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 26 Mar 2013
Posts: 12
Location: United States
Followers: 0

Kudos [?]: 11 [0], given: 3

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 12 Jun 2013, 15:26
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.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33075
Followers: 5777

Kudos [?]: 70917 [1] , given: 9857

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 12 Jun 2013, 15:43
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.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 26 Mar 2013
Posts: 12
Location: United States
Followers: 0

Kudos [?]: 11 [0], given: 3

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 12 Jun 2013, 18:52
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.
Intern
Intern
avatar
Joined: 26 Dec 2012
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 16 Nov 2013, 21:35
any prime number greater than 3, can be written as either (6n+1) or (6n-1).
Director
Director
User avatar
Joined: 23 Jan 2013
Posts: 513
Schools: Cambridge'16
Followers: 2

Kudos [?]: 50 [0], given: 37

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 12 Sep 2014, 02:03
The only pair having common factor except 1 and itself is 6!+21, they both divisible by 3. So their sum cannot be prime

B
SVP
SVP
avatar
Joined: 17 Jul 2014
Posts: 1615
Location: United States
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.56
WE: General Management (Transportation)
Followers: 10

Kudos [?]: 164 [0], given: 104

GMAT ToolKit User Premium Member Reviews Badge
Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 17 Sep 2014, 12:19
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.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9708
Followers: 467

Kudos [?]: 120 [0], given: 0

Premium Member
Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 21 Sep 2015, 18:02
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

Expert Post
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 380
Location: India
GMAT 1: 760 Q50 V44
Followers: 13

Kudos [?]: 140 [0], given: 9

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 22 Sep 2015, 01:21
Expert's post
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
_________________

Reach out to us at bondwithus@gmatify.com

Image

Intern
Intern
avatar
Joined: 22 Sep 2015
Posts: 3
Followers: 0

Kudos [?]: 1 [0], given: 29

Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 22 Sep 2015, 09:18
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

So answer B
Expert Post
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 380
Location: India
GMAT 1: 760 Q50 V44
Followers: 13

Kudos [?]: 140 [1] , given: 9

Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 22 Sep 2015, 23:39
1
This post received
KUDOS
Expert's post
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

So answer B


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.
_________________

Reach out to us at bondwithus@gmatify.com

Image

Director
Director
User avatar
Joined: 12 Aug 2015
Posts: 686
Followers: 10

Kudos [?]: 64 [0], given: 160

GMAT ToolKit User CAT Tests
Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 22 Apr 2016, 10:23
Primes cannot be written as a product of two numbers
Smash B
Stone Cold
Math Forum Moderator
User avatar
Joined: 11 Jun 2011
Posts: 918
Location: India
Concentration: International Business, Finance
Schools: ISB '18
WE: Corporate Finance (Commercial Banking)
Followers: 19

Kudos [?]: 192 [0], given: 169

GMAT ToolKit User Premium Member CAT Tests
Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 22 Apr 2016, 12:55
stonecold wrote:
Primes cannot be written as a product of two numbers
Smash B
Stone Cold


Nothing just respect for you :wave

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 !!
_________________

“Give me some sunshine
Give me some rain
Give me another chance
I wanna grow up once again.”


Abhishek....

Which of the following numbers is not prime ?   [#permalink] 22 Apr 2016, 12:55
    Similar topics Author Replies Last post
Similar
Topics:
60 Experts publish their posts in the topic Which of the following numbers is prime? honchos 15 01 Mar 2014, 23:56
5 Experts publish their posts in the topic If a and b are prime numbers, which of the following CANNO emmak 6 11 Mar 2013, 23:32
8 Experts publish their posts in the topic If n is a prime number and n ≠ 3, which of the following Jp27 9 03 Nov 2012, 01:49
5 Experts publish their posts in the topic If x and y are prime numbers, which of the following CANNOT fiendex 8 06 Feb 2012, 04:14
23 Experts publish their posts in the topic Which of the following CANNOT be the sum of two prime numbers? banksy 6 17 Feb 2011, 15:10
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  


GMAT Club MBA Forum Home| About| 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®.