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

It is currently 18 Aug 2018, 05:22

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

If x is the smallest positive integer that is not prime and

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

Hide Tags

Intern
Intern
avatar
Joined: 04 Jun 2013
Posts: 2
If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 30 Jul 2013, 12:07
7
50
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (01:15) correct 66% (01:07) wrong based on 826 sessions

HideShow timer Statistics

If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?

A. 51
B. 54
C. 72
D. 162
E. 50!+2
Most Helpful Expert Reply
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12189
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 08 Feb 2018, 12:09
2
Hi All,

50! = (1)(2)(3)(4)....(48)(49)(50)

50! is clearly divisible by LOTS of different integers. Besides the 50 integers listed above, ANY integer that can be created by multiplying any of those values (or their factors) will divide into 50!

For example:
(2) and (49) are both factors of 50!, so (2)(49) = 98 will ALSO be a factor of 50!.

The question asks us to find the SMALLEST positive integer that is NOT PRIME and NOT a factor of 50! Once we have that value, we have to figure out the sum of its factors.

Rather than try to list out all of the possible factors of 50!, we have to think about the type of number that is NOT a factor of 50! If we think about prime-factorization, we'll find that the smallest prime factor in 50! is 2 (it can be found in ALL of the even integers). Similarly, we can find '3' in all of the multiples of 3 (3, 6, 9, etc.) and we can find '5' in all of the multiples of 5 (5, 10, 15, etc.). The largest prime factor in 50! is 47; to find a number that is NOT a factor of 50!, we have to find one that includes a prime factor that is NOT a factor of 50!

The next largest prime number above 47 is 53. 53 is NOT a factor of 50! and we cannot 'get to' 53 by multiplying any of the factors of 50! The prompt tells us that we need a number that is NOT prime though - the smallest number that has 53 as a factor and is NOT prime is 106 (which is 2x53). THAT is the smallest number that fits all of the restrictions that we're given.

From there, we know two of the factors of 106 already: 1 and 106, so the sum has to be GREATER THAN 106. The only answer among the 5 choices that makes any sense is....

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Most Helpful Community Reply
Intern
Intern
avatar
Joined: 24 Nov 2013
Posts: 3
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 12 Dec 2013, 05:50
5
Factors of 50!: 1,2,3,......,50

If x is not a factor of 50! then one of his primes must be bigger than 49 ( the largest prime of 50!).

The next prime is 53.Thus x must be a multiple of 53.

Since x is not a prime the smallest possible multiple of 53 is 53 * 2 = 106

Sum of his factors: 1+2+53+106 = 162

Hope i helped :)
General Discussion
Founder
Founder
User avatar
V
Joined: 04 Dec 2002
Posts: 17230
Location: United States (WA)
GMAT 1: 750 Q49 V42
GMAT ToolKit User CAT Tests
Re: Doubt: GMAT Number Theory Question  [#permalink]

Show Tags

New post 30 Jul 2013, 16:06
Moving to the proper sub-forum.
Please post gmat question discussions in the proper sub-forums.
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here...
OG2019 Directory is here! - New!
Verbal OG2019 Directory is here! - New!

Co-author of the GMAT Club tests

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47981
Re: Doubt: GMAT Number Theory Question  [#permalink]

Show Tags

New post 31 Jul 2013, 00:47
16
7
brianlange77 wrote:
If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?

A. 51
B. 54
C. 72
D. 162
E. 50!+2

Thanks for posting -- would be great for you to post the source of the question for easier reference in the future. That said, the factors of 50! are all the numbers from 1-50. The smallest positive integer that is not prime and not a factor of 50! is therefore 51. The factors of 51 are 1, 3, 17, and 51. The sum of those four numbers is 72.

Thoughts?

-Brian


In fact 51=3*17 IS a factor of 50!.

The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.

Answer: D.
_________________

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

VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1096
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 31 Jul 2013, 06:34
1
brianlange77 wrote:
Just for the sake of debate --- explain to me again how the number 51 (not its factors, but the number itself) is a factor of 50!?
Thanks.
-Brian


If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?

If \(x=51\), then \(x\) is a factor of \(50!\), \(\frac{50!}{51}=integer\). I do not get what you mean by "not its factors, but the number itself"...

Do you mean something like \(50!=1*2*4*...*16*...*18*...*50\)[all numbers except 3 and 17]\(*51\) ? (so you see the 51 in the number 50! ?)
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Manhattan Prep Instructor
User avatar
Joined: 01 Jul 2013
Posts: 194
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 31 Jul 2013, 06:38
2
Ahh... total mis-read on my part. Good work!
_________________


Brian Lange | Manhattan GMAT Instructor | North Carolina


Manhattan GMAT Discount | Manhattan GMAT Course Reviews | View Instructor Profile

Manager
Manager
avatar
Joined: 12 Feb 2012
Posts: 125
Re: Doubt: GMAT Number Theory Question  [#permalink]

Show Tags

New post 31 Jul 2013, 14:20
Bunuel wrote:
brianlange77 wrote:
If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?

A. 51
B. 54
C. 72
D. 162
E. 50!+2

Thanks for posting -- would be great for you to post the source of the question for easier reference in the future. That said, the factors of 50! are all the numbers from 1-50. The smallest positive integer that is not prime and not a factor of 50! is therefore 51. The factors of 51 are 1, 3, 17, and 51. The sum of those four numbers is 72.

Thoughts?

-Brian


In fact 51=3*17 IS a factor of 50!.

The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.

Answer: D.


Bunuel,

How did you know it was 106=53*2? What is the thought process.

53 is a prime a number, obviously not in 50!. 53 cannot be the answer because the number must not be a factor of 50! and not a prime. How do you know for sure that there are not any numbers between 51 and 106 that might satisfy the condition?
Manhattan Prep Instructor
User avatar
Joined: 01 Jul 2013
Posts: 194
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 31 Jul 2013, 17:59
2
1
I'll start the answer process for you....

-51 has factors of 3 and 17, so that's out, because those are both factors of 50!
-52 has factors of 2 (twice) and 13, so that's out...
-53 is not a factor of 50!, but it's prime :-(
-But, 106 (which is 2*53) is the next smallest choice (any other non-factors between 53 and 106 would also be prime, violating the terms of the problem.)

Thoughts?
_________________


Brian Lange | Manhattan GMAT Instructor | North Carolina


Manhattan GMAT Discount | Manhattan GMAT Course Reviews | View Instructor Profile

Intern
Intern
avatar
Joined: 04 Jul 2013
Posts: 16
Location: India
Concentration: Operations, Technology
WE: Operations (Manufacturing)
GMAT ToolKit User
Re: Doubt: GMAT Number Theory Question  [#permalink]

Show Tags

New post 01 Aug 2013, 02:27
Bunuel wrote:
brianlange77 wrote:
If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?

A. 51
B. 54
C. 72
D. 162
E. 50!+2

Thanks for posting -- would be great for you to post the source of the question for easier reference in the future. That said, the factors of 50! are all the numbers from 1-50. The smallest positive integer that is not prime and not a factor of 50! is therefore 51. The factors of 51 are 1, 3, 17, and 51. The sum of those four numbers is 72.

Thoughts?

-Brian


In fact 51=3*17 IS a factor of 50!.

The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.

Answer: D.



Yes Bunuel you absolutely correct the answer should be D...
Manager
Manager
avatar
Joined: 30 May 2013
Posts: 168
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
GMAT ToolKit User
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 01 Aug 2013, 11:01
brianlange77 wrote:
I'll start the answer process for you....

-51 has factors of 3 and 17, so that's out, because those are both factors of 50!
-52 has factors of 2 (twice) and 13, so that's out...
-53 is not a factor of 50!, but it's prime :-(
-But, 106 (which is 2*53) is the next smallest choice (any other non-factors between 53 and 106 would also be prime, violating the terms of the problem.)

Thoughts?

Hi Brain,

In this case 106 which is 2*53 but 2 is a factor of 50! as in the previous case of 51 was out because 3 and 17 were factors of 50!.

can u explain y answer is 106 even 2 is in factor of 50!?

regards,
RRSNATHAN
Intern
Intern
avatar
Joined: 02 Feb 2012
Posts: 27
GPA: 4
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 01 Aug 2013, 19:26
rrsnathan wrote:
brianlange77 wrote:
I'll start the answer process for you....

-51 has factors of 3 and 17, so that's out, because those are both factors of 50!
-52 has factors of 2 (twice) and 13, so that's out...
-53 is not a factor of 50!, but it's prime :-(
-But, 106 (which is 2*53) is the next smallest choice (any other non-factors between 53 and 106 would also be prime, violating the terms of the problem.)

Thoughts?

Hi Brain,

In this case 106 which is 2*53 but 2 is a factor of 50! as in the previous case of 51 was out because 3 and 17 were factors of 50!.

can u explain y answer is 106 even 2 is in factor of 50!?

regards,
RRSNATHAN


The number in discussion is 106. We need to see if that number is a factor of 50! or not.
We need not worry about 2 being a factor right...

Eg: (100/14) => 50*2/7*2
Does not imply 14 is a factor of 100...
Manager
Manager
avatar
Joined: 30 May 2013
Posts: 168
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
GMAT ToolKit User
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 20 Aug 2013, 23:34
avinashrao9 wrote:
rrsnathan wrote:
brianlange77 wrote:
I'll start the answer process for you....

-51 has factors of 3 and 17, so that's out, because those are both factors of 50!
-52 has factors of 2 (twice) and 13, so that's out...
-53 is not a factor of 50!, but it's prime :-(
-But, 106 (which is 2*53) is the next smallest choice (any other non-factors between 53 and 106 would also be prime, violating the terms of the problem.)

Thoughts?

Hi Brain,

In this case 106 which is 2*53 but 2 is a factor of 50! as in the previous case of 51 was out because 3 and 17 were factors of 50!.

can u explain y answer is 106 even 2 is in factor of 50!?

regards,
RRSNATHAN


The number in discussion is 106. We need to see if that number is a factor of 50! or not.
We need not worry about 2 being a factor right...

Eg: (100/14) => 50*2/7*2
Does not imply 14 is a factor of 100...



Hi anybody pls explain this

Still i am not clear in this.

In explanation it is mentioned as
-51 has factors of 3 and 17, so that's out, because those are both factors of 50!
Here its mentioned as 3 and 17 are the factors of 59!.

In the same way 106 has two factors 2 and 53 in this 2 is the factor of 50! or not??

plz explain this.


Thanks in advance,
-Rrsnathan
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47981
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 21 Aug 2013, 02:36
rrsnathan wrote:
avinashrao9 wrote:
rrsnathan wrote:
Hi Brain,

In this case 106 which is 2*53 but 2 is a factor of 50! as in the previous case of 51 was out because 3 and 17 were factors of 50!.

can u explain y answer is 106 even 2 is in factor of 50!?

regards,
RRSNATHAN


The number in discussion is 106. We need to see if that number is a factor of 50! or not.
We need not worry about 2 being a factor right...

Eg: (100/14) => 50*2/7*2
Does not imply 14 is a factor of 100...



Hi anybody pls explain this

Still i am not clear in this.

In explanation it is mentioned as
-51 has factors of 3 and 17, so that's out, because those are both factors of 50!
Here its mentioned as 3 and 17 are the factors of 59!.

In the same way 106 has two factors 2 and 53 in this 2 is the factor of 50! or not??

plz explain this.


Thanks in advance,
-Rrsnathan


Your question is not clear.

x is the smallest positive integer that is not prime and not a factor of 50! --> x=106 --> 106 is NOT a prime and is NOT a factor of 50!.
_________________

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

Manager
Manager
avatar
Joined: 30 May 2013
Posts: 168
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
GMAT ToolKit User
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post Updated on: 21 Aug 2013, 03:59
Hi,

Thanks for the explanation.

106 is NOT a prime and is NOT a factor of 50!
if this ur explanation

Then 51! is also not factor of 50! and not prime too. For omitting this we had an explanation as " 51 has factors of 3 and 17, so that's out, because those are both factors of 50!"

The same explanation will go for 106 - as 106 has factors 2 and 53, 2 is factors of 50! right?

Please explain this.

Thanks in advance,
Rrsnathan.

Originally posted by rrsnathan on 21 Aug 2013, 03:52.
Last edited by rrsnathan on 21 Aug 2013, 03:59, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47981
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 21 Aug 2013, 03:59
1
rrsnathan wrote:
Hi,

Thanks for the explanation.

106 is NOT a prime and is NOT a factor of 50!
if this ur explanation

Then 51! is also not factor of 50! and not prime too. For omitting this we had an explanation as " 51 has factors of 3 and 17, so that's out, because those are both factors of 50!"

The same explanation will go for 106 - as 106 has factors 2 and 53, both are in factors of 50! right?

Please explain this.

Thanks in advance,
Rrsnathan.


No. 53 is NOT a factor of 50!
_________________

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

Manager
Manager
avatar
Joined: 30 May 2013
Posts: 168
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
GMAT ToolKit User
Re: If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 21 Aug 2013, 04:06
Bunuel wrote:
rrsnathan wrote:
Hi,

Thanks for the explanation.

106 is NOT a prime and is NOT a factor of 50!
if this ur explanation

Then 51! is also not factor of 50! and not prime too. For omitting this we had an explanation as " 51 has factors of 3 and 17, so that's out, because those are both factors of 50!"

The same explanation will go for 106 - as 106 has factors 2 and 53, both are in factors of 50! right?

Please explain this.

Thanks in advance,
Rrsnathan.


No. 53 is NOT a factor of 50!


Perfectly understood.

Thanks a lot Bunuel.
Intern
Intern
avatar
Joined: 26 Aug 2013
Posts: 11
If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 01 Aug 2014, 04:38
If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?
A. 51
B. 54
C. 72
D. 162
E. 50!+2

This question has been discussed before, but I could not understand something from Bunuel's reply.
he said
In fact 51=3*17 IS a factor of 50!.
The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.

I understand that 53 is not factor of 50! since it is prime,, so multiplying by 2 make 53 not prime and not factor of 50! as well.
But, can someone explain how we can tell that none between 53 and 106 is not factor of 50!?
Is it becuase only prime numbers greater than 50 is not factors of 50!
so the smallest prime greater than 50 is 53 and thus 106 is smallest ineter that is NOT prime and NOT a factor of 50!?

Let me know please.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47981
If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 01 Aug 2014, 06:54
2
sehosayho wrote:
If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?
A. 51
B. 54
C. 72
D. 162
E. 50!+2

This question has been discussed before, but I could not understand something from Bunuel's reply.
he said
In fact 51=3*17 IS a factor of 50!.
The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.

I understand that 53 is not factor of 50! since it is prime,, so multiplying by 2 make 53 not prime and not factor of 50! as well.
But, can someone explain how we can tell that none between 53 and 106 is not factor of 50!?
Is it becuase only prime numbers greater than 50 is not factors of 50!
so the smallest prime greater than 50 is 53 and thus 106 is smallest ineter that is NOT prime and NOT a factor of 50!?

Let me know please.


All numbers between 50 and 106, are either primes (and we know that x is NOT a prime) or factors of 50!, because it has all their primes in higher powers. For example:

59 is a prime, hence x cannot be 59.
60 = 2^2*3*5. 50! will for sure have 2, 3, and 5 in higher power than 2, 1 and 1, respectively.

Hope it's clear.

P.S. Please do not double post a topic, put your questions in existing one. Thank you.
_________________

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

Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 637
Location: India
If x is the smallest positive integer that is not prime and  [#permalink]

Show Tags

New post 02 Aug 2014, 17:54
4
The first number after n that will not be a factor of n! is the first prime after n. If the number cannot be a prime, then the first number that will not be a factor of n! is the p*2, where p is the first prime after n.

So in our case x will be 53*2=106 and the sum of the factors of 106 is 162.
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

If x is the smallest positive integer that is not prime and &nbs [#permalink] 02 Aug 2014, 17:54

Go to page    1   2    Next  [ 36 posts ] 

Display posts from previous: Sort by

If x is the smallest positive integer that is not prime and

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.