It is currently 23 Oct 2017, 03:18

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.

Close

Request Expert Reply

Confirm Cancel

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

2 KUDOS received
Manager
Manager
avatar
Joined: 17 Sep 2011
Posts: 191

Kudos [?]: 139 [2], given: 8

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

Show Tags

New post 03 May 2012, 01:14
2
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (00:59) correct 31% (01:10) wrong based on 420 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

Kudos [?]: 139 [2], given: 8

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41910

Kudos [?]: 129407 [3], given: 12201

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

Show Tags

New post 03 May 2012, 01:21
3
This post received
KUDOS
Expert's post
2
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


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: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 129407 [3], given: 12201

Manager
Manager
avatar
Joined: 02 Jun 2011
Posts: 150

Kudos [?]: 104 [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?

Kudos [?]: 104 [0], given: 11

Expert Post
6 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7677

Kudos [?]: 17399 [6], given: 232

Location: Pune, India
Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 03 May 2012, 09:38
6
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

Kudos [?]: 17399 [6], given: 232

Intern
Intern
avatar
Joined: 25 Jun 2012
Posts: 36

Kudos [?]: 30 [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.

Kudos [?]: 30 [0], given: 4

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41910

Kudos [?]: 129407 [0], given: 12201

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

Show Tags

New post 12 Jun 2013, 05:25
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: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 129407 [0], given: 12201

Intern
Intern
avatar
Joined: 26 Mar 2013
Posts: 12

Kudos [?]: 13 [0], given: 3

Location: United States
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.

Kudos [?]: 13 [0], given: 3

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41910

Kudos [?]: 129407 [1], given: 12201

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: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 129407 [1], given: 12201

Intern
Intern
avatar
Joined: 26 Mar 2013
Posts: 12

Kudos [?]: 13 [0], given: 3

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

Show Tags

New post 12 Jun 2013, 18:52
1
This post was
BOOKMARKED
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.

Kudos [?]: 13 [0], given: 3

Expert Post
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 396

Kudos [?]: 337 [0], given: 10

Location: India
GMAT 1: 760 Q50 V44
Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 22 Sep 2015, 01:21
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

Kudos [?]: 337 [0], given: 10

Intern
Intern
avatar
Joined: 22 Sep 2015
Posts: 6

Kudos [?]: 1 [0], given: 49

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

Kudos [?]: 1 [0], given: 49

Expert Post
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 396

Kudos [?]: 337 [1], given: 10

Location: India
GMAT 1: 760 Q50 V44
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

Kudos [?]: 337 [1], given: 10

BSchool Forum Moderator
User avatar
P
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 845 [0], given: 595

GMAT ToolKit User Premium Member 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
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 845 [0], given: 595

Math Forum Moderator
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3003

Kudos [?]: 1088 [0], given: 325

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
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 !!
_________________

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 )

Kudos [?]: 1088 [0], given: 325

Manager
Manager
avatar
S
Joined: 27 Aug 2016
Posts: 95

Kudos [?]: 4 [0], given: 149

Location: India
Schools: HEC Montreal '21
GMAT 1: 670 Q47 V37
GPA: 3
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: Which of the following numbers is not prime ? [#permalink]

Show Tags

New post 24 Dec 2016, 10:39
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?

Kudos [?]: 4 [0], given: 149

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 776

Kudos [?]: 41 [0], given: 268

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

Show Tags

New post 03 Apr 2017, 23:55
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.

Kudos [?]: 41 [0], given: 268

Re: Which of the following numbers is not prime ?   [#permalink] 03 Apr 2017, 23:55
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 | Emoji artwork provided by EmojiOne

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®.