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

It is currently 06 Dec 2019, 09:23

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

M31-11

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
M31-11  [#permalink]

Show Tags

New post 09 Jun 2015, 07:49
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

78% (00:50) correct 22% (00:33) wrong based on 36 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
Re M31-11  [#permalink]

Show Tags

New post 09 Jun 2015, 07:50
Official Solution:

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


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 therefore 2*31=62. Notice that all numbers between 30 and 62, are either primes (and we know that x is NOT a prime) or factors of 30! (because 30! has all their primes in higher powers). For example:

31 is a prime, hence x cannot be 31.

\(32 = 2^5\). 30! will for sure have 2 in higher power than 5, hence 32 IS a factor of 30!.

\(33 = 3*11\). Both 3 and 11 are factors of 30!, hence 33 IS a factor of 30!

...

\(64= 2^6\). 30! will for sure have 2 in higher power than 6, hence 64 IS a factor of 30!.


Answer: D
_________________
Intern
Intern
avatar
B
Joined: 05 Feb 2017
Posts: 2
Re: M31-11  [#permalink]

Show Tags

New post 29 Dec 2017, 15:35
Tricky dicky
Manager
Manager
avatar
G
Joined: 16 May 2016
Posts: 198
Location: India
Concentration: Marketing, International Business
Schools: ESSEC '21 (A$)
GMAT 1: 720 Q50 V38
GPA: 3.5
WE: Analyst (Consulting)
Re: M31-11  [#permalink]

Show Tags

New post 17 Jun 2018, 20:04
Bunuel wrote:
Official Solution:

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


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 therefore 2*31=62. Notice that all numbers between 30 and 62, are either primes (and we know that x is NOT a prime) or factors of 30! (because 30! has all their primes in higher powers). For example:

31 is a prime, hence x cannot be 31.

\(32 = 2^5\). 30! will for sure have 2 in higher power than 5, hence 32 IS a factor of 30!.

\(33 = 3*11\). Both 3 and 11 are factors of 30!, hence 33 IS a factor of 30!

...

\(64= 2^6\). 30! will for sure have 2 in higher power than 6, hence 64 IS a factor of 30!.


Answer: D


I somehow did not understand this explanation.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
Re: M31-11  [#permalink]

Show Tags

New post 17 Jun 2018, 20:07
Cbirole wrote:
Bunuel wrote:
Official Solution:

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


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 therefore 2*31=62. Notice that all numbers between 30 and 62, are either primes (and we know that x is NOT a prime) or factors of 30! (because 30! has all their primes in higher powers). For example:

31 is a prime, hence x cannot be 31.

\(32 = 2^5\). 30! will for sure have 2 in higher power than 5, hence 32 IS a factor of 30!.

\(33 = 3*11\). Both 3 and 11 are factors of 30!, hence 33 IS a factor of 30!

...

\(64= 2^6\). 30! will for sure have 2 in higher power than 6, hence 64 IS a factor of 30!.


Answer: D


I somehow did not understand this explanation.


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.

Check more solutions here: https://gmatclub.com/forum/what-is-the- ... 98237.html

Hope it helps.
_________________
LBS Moderator
User avatar
V
Joined: 04 Jun 2018
Posts: 663
Location: Germany
Concentration: General Management, Finance
GMAT 1: 730 Q47 V44
GPA: 3.4
WE: Analyst (Transportation)
Reviews Badge
Re: M31-11  [#permalink]

Show Tags

New post 27 Sep 2018, 03:59
The fact that we are directly told to look for a none prime number does give us the key to solving this question.

As we know 31 is a prime number, we can look for the next smallest answer choice that does contain a prime factor which is not part of 30!.
Once we see that 62 = 2x31 we know we have found our right answer.

Best regards,
Chris
_________________
GMAT Club Bot
Re: M31-11   [#permalink] 27 Sep 2018, 03:59
Display posts from previous: Sort by

M31-11

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

Moderators: chetan2u, Bunuel






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