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

It is currently 12 Dec 2018, 17:51

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

What is the least positive integer that is not a factor of 30! and is

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51121
What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 14 May 2015, 04:03
1
7
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (00:48) correct 32% (00:36) wrong based on 205 sessions

HideShow timer Statistics

Most Helpful Community Reply
Manager
Manager
avatar
S
Joined: 13 Nov 2014
Posts: 109
GMAT 1: 740 Q50 V40
Reviews Badge
Re: What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 14 May 2015, 05:20
5
Bunuel wrote:
What is the least positive integer that is not a factor of 30! and is not a prime number?

A. 31
B. 32
C. 33
D. 62
E. 64

Kudos for a correct solution.



Not reading carefully is going to kill me on the GMAT. My instinct was to select A because I missed the "NOT A PRIME NUMBER" part.

If you do not know what you're looking for, the best way to go about this problem is by breaking down each of the options into factors.

A) 31 is prime and per the question stem we cannot use this
B) 32 = 2 * 16 - within 30! we have a 2 and 16 so 32 will be a factor of 30!
C) 33 = 3 *11 - again within 30! we have a 3 and an 11 so 33 will be a factor of 30!
D) 62 = 31 * 2 - Bingo 31 is not included in 30!
E) 64 = 16 * 4 - both 16 and 4 are multiplied in 30!


Answer is D!
_________________

Gmat prep 1 600
Veritas 1 650
Veritas 2 680
Gmat prep 2 690 (48Q 37V)
Gmat prep 5 730 (47Q 42V)
Gmat prep 6 720 (48Q 41V)

General Discussion
Intern
Intern
avatar
Joined: 03 Dec 2014
Posts: 15
GMAT 1: 620 Q43 V32
GPA: 2.9
GMAT ToolKit User Premium Member Reviews Badge
Re: What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 14 May 2015, 04:06
Bunuel wrote:
What is the least positive integer that is not a factor of 30! and is not a prime number?

A. 31
B. 32
C. 33
D. 62
E. 64

Kudos for a correct solution.


Should be 32 since 31 is a prime.
Intern
Intern
User avatar
Joined: 29 Apr 2013
Posts: 11
GMAT ToolKit User
What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 14 May 2015, 04:25
1
1
D is the answer (62=31•2 is not a factor)

30!= 1•2•3•...11•..16•..29•30

A) 31 prime number
B) 32=16•2 factor
C) 33=11•3 factor
E)64= 16•4 factor

Image Posted from GMAT ToolKit
_________________

“It’s not that I’m so smart; it’s just that I stay with problems longer.” - Albert Einstein
"Kirib chiqma, bilib chiq."
"Век живи́ - век учи́сь."

Senior Manager
Senior Manager
avatar
Joined: 02 Mar 2012
Posts: 310
Schools: Schulich '16
What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 14 May 2015, 07:18
2
its D.

as 30 and 31 are co primes 31 will be the positive integer hat wont be a factor of 31!

but wait, question asks us that positive integer shouldnt be prime.

So find multiples of 31 as rest all other numbers in choices would be divisibleby 30! or be a prime.

therefore, 62=31*2

hope it helps
Senior Manager
Senior Manager
User avatar
S
Joined: 21 Jan 2015
Posts: 355
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)
GMAT ToolKit User CAT Tests
Re: What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 14 May 2015, 19:36
Bunuel wrote:
What is the least positive integer that is not a factor of 30! and is not a prime number?

A. 31
B. 32
C. 33
D. 62
E. 64


Ans: D

Solution: 30! includes integer from 1-30 in multiplication form. means any value turning out to be a multiplication of this range can not be the ans and ofcourse any prime number too.
A) 31= prime number; not an answer
B) 32 = 16*2 = not an answer as 30! contains 16 and 2 in it.
C) 33 = 11*3 = not an answer
D) 62 = 31*2 = Correct as 31 is not in 30!
E) 64 = 16*4 = not an answer

Ans : D
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13065
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 14 May 2015, 21:53
Hi SD007,

You have to be very careful with this question. The answer that you chose is the one that is "the least number greater than 30 that is NOT prime"...but it's not the answer to THIS question.

30! = (30)(29)(28)(27)....(3)(2)(1)

So we're dealing with a gigantic number that is divisible by a LOT of other numbers.

For example, we know that 30! is divisible by 60 because 30! has a (30) and a (2) in it, and (30)(2) is 60.

That same logic can help you to eliminate each of the wrong answers (besides 31, since 31 is prime and we're told to find a value that is NOT prime).

32 = (16)(2) so it too is a factor of 30! Can you eliminate the other wrong answers in the same way?

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!*****

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8665
Location: Pune, India
Re: What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 14 May 2015, 22:09
1
1
Celestial09 wrote:
Hi,
Couldn't understood the question yet...
waiting for the explanation and OA.
thanks
celetial


30! = 1*2*3*4*5*...*28*29*30
So all the numbers from 1 to 30 are factors of 30!. Also, all numbers which you can make by combining these factors are factors of 30!
So 2*29 = 58 is a factor of 30!, 2*4*8 = 64 is a factor of 30! and so on...

You want a number which is not a factor of 30!
The smallest number that is not a factor of 30! is 31. But it is a prime number. You want the smallest number that is not a factor of 30! and is not prime. So the next smallest such number would be 31*2 = 62.

Now think why no other number between 31 and 62 can be number which is not a factor of 30! and not prime.
32 = 4*8 (both factors of 30! so 32 is a factor of 30!)
33 = 3*11 (both factors of 30! so 33 is a factor of 30!)
34 = 2*17 (both factors of 30! so 34 is a factor of 30!)
and so on...
37 = 37 (prime)
and so on...
Basically, you want the number to be composed of two numbers such that at least one of them is not a factor of 30!. The first such number is 31. You multiply it by the smallest number 2 to get a non prime number which is not divisible by 30!.

Answer (D)

Do focus a bit on this logic. To solve the question, you can use the options of course!
_________________

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 >

Manager
Manager
User avatar
Status: Kitchener
Joined: 03 Oct 2013
Posts: 89
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Premium Member
Re: What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 15 May 2015, 16:40
the answer is D

31 is prime
B) 32 = 4*8 both are a factors of 30!
C) 33 = 3 *11 both are a factors of 30!
E) 64 = 16 * 4 both are a factors of 30!
so D
_________________

Click +1 Kudos if my post helped

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51121
What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 18 May 2015, 06:28
Bunuel wrote:
What is the least positive integer that is not a factor of 30! and is not a prime number?

A. 31
B. 32
C. 33
D. 62
E. 64

Kudos for a correct solution.


OFFICIAL SOLUTION:

We need such number which is not a factor of 30! and is not a prime number.

The smallest prime which is not a factor of 30! is obviously 31. So, the smallest positive integer that is not a factor of 30! and is not a prime number is 2*31=62.

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9138
Premium Member
Re: What is the least positive integer that is not a factor of 30! and is  [#permalink]

Show Tags

New post 01 Oct 2018, 06:09
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

GMAT Club Bot
Re: What is the least positive integer that is not a factor of 30! and is &nbs [#permalink] 01 Oct 2018, 06:09
Display posts from previous: Sort by

What is the least positive integer that is not a factor of 30! and is

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


cron
Copyright

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®.