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

It is currently 17 Aug 2018, 04:14

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47961
M31-11  [#permalink]

Show Tags

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

Difficulty:

  35% (medium)

Question Stats:

75% (00:46) correct 25% (00:44) wrong based on 28 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47961
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
_________________

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

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
S
Joined: 16 May 2016
Posts: 130
Location: India
Concentration: Marketing, Healthcare
GPA: 3
WE: Analyst (Computer Software)
CAT Tests
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.
_________________

Not Giving UP! Kudos if you like the question :)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47961
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.
_________________

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

Re: M31-11 &nbs [#permalink] 17 Jun 2018, 20:07
Display posts from previous: Sort by

M31-11

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

Moderators: chetan2u, Bunuel

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®.