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

 It is currently 23 May 2019, 22:45 ### 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. ### Request Expert Reply # M31-11

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

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55276
M31-11  [#permalink]

### Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 76% (00:50) correct 24% (00:33) wrong based on 33 sessions

### HideShow timer Statistics

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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 55276
Re M31-11  [#permalink]

### Show Tags

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  B
Joined: 05 Feb 2017
Posts: 2
Re: M31-11  [#permalink]

### Show Tags

Tricky dicky
Manager  G
Joined: 16 May 2016
Posts: 202
Location: India
Concentration: Marketing, Healthcare
GPA: 3.5
WE: Analyst (Consulting)
Re: M31-11  [#permalink]

### Show Tags

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.
_________________
Not Giving UP! Kudos if you like the question Math Expert V
Joined: 02 Sep 2009
Posts: 55276
Re: M31-11  [#permalink]

### Show Tags

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.
_________________
Senior Manager  D
Joined: 04 Jun 2018
Posts: 472
Location: Germany
Concentration: General Management, Finance
GPA: 3.6
WE: Analyst (Transportation)
Re: M31-11  [#permalink]

### Show Tags

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
_________________
A couple of things that helped me in verbal:
https://gmatclub.com/forum/verbal-strategies-268700.html#p2082192

Gmat Prep CAT #1: V42, Q34, 630
Gmat Prep CAT #2: V46, Q35, 660
Gmat Prep CAT #3: V41, Q42, 680

On the mission to improve my quant score, all help is appreciated!  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 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®.

#### MBA Resources  