NEW HERE? LEARN MORE
closeclose
It is currently 18 Apr 2024, 11:34
Register
GMAT Focus Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If a is divisible by 6!, then a/5 must be

10 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Question banks

GMAT Question Banks

Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92747
CAT Tests Forum Quiz Mode
If a is divisible by 6!, then a/5 must be [#permalink] New post  06 Dec 2016, 07:31
3
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

73% (01:19) correct 27% (01:25) wrong based on 200 sessions
Hide Show timer Statistics
If a is divisible by 6!, then a/5 must be

I. a prime number
II. divisible by 3
III. a multiple of 5

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6073
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
GMAT ToolKit User
Re: If a is divisible by 6!, then a/5 must be [#permalink] New post  06 Dec 2016, 07:55
1
Kudos
Bunuel wrote:
If a is divisible by 6!, then a/5 must be

I. a prime number
II. divisible by 3
III. a multiple of 5

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III


Least value of a = 720

Now, a/5 = 144 ( Divisible by 3 )

Let value of a = 1440

Now, a/5 = 288 ( Divisible by 3 )

Answer will be (B) Only II...
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Signature Read More
avatar
S
ehsan090
Manager
Manager
Joined: 08 Oct 2016
Posts: 185
Location: United States
Concentration: General Management, Finance
GPA: 2.9
WE:Engineering (Telecommunications)
Re: If a is divisible by 6!, then a/5 must be [#permalink] New post  18 Apr 2017, 05:23
Abhishek009 wrote:
Bunuel wrote:
If a is divisible by 6!, then a/5 must be

I. a prime number
II. divisible by 3
III. a multiple of 5

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III


Least value of a = 720

Now, a/5 = 144 ( Divisible by 3 )

Let value of a = 1440

Now, a/5 = 288 ( Divisible by 3 )

Answer will be (B) Only II...


Hi tell me one thing since least value of a is 720 so it should be multiple of 5 as well
Please explain Abhishek009
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92747
CAT Tests Forum Quiz Mode
Re: If a is divisible by 6!, then a/5 must be [#permalink] New post  18 Apr 2017, 05:27
Expert Reply
ehsan090 wrote:
Abhishek009 wrote:
Bunuel wrote:
If a is divisible by 6!, then a/5 must be

I. a prime number
II. divisible by 3
III. a multiple of 5

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III


Least value of a = 720

Now, a/5 = 144 ( Divisible by 3 )

Let value of a = 1440

Now, a/5 = 288 ( Divisible by 3 )

Answer will be (B) Only II...


Hi tell me one thing since least value of a is 720 so it should be multiple of 5 as well
Please explain Abhishek009


The least value of a is 6! = 720, but we are asked about a/5, not a. The least value of a/5 is 6!/5 = 144.

Hope it's clear.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
D
stonecold
Alum
Joined: 12 Aug 2015
Posts: 2284
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: If a is divisible by 6!, then a/5 must be [#permalink] New post  18 Apr 2017, 05:42
2
Kudos
1
Bookmarks
Hi ehsan090
It is not necessary to compute this value 720 at all here.
Its good to remember factorials upto 6.
But i did not depend on my knowledge to remember that 6! is 720.


Simply put let a=6!(smallest value)

So we are asked about a/5

Statement 1=>
a/5 will never be a prime.There would be a lot of other integers in the numerator--> 2,3,4 etc.
Hence this is false
Statement 2 =>
a/5 will take aways the five from 6!
But three would always be there in the numerator.
Hence this is always true.

Statement 2 =>
a/5 may or may not contain 5.
Example if a=6! then a/5 will be 1*2*3*4*6.
We don't have any five here.
Hence this statement may or may be true.

((This statement can be true if a was say 6!*5 ))



Smash that B.
_________________
Give me a hell yeah ...!!!!!

MBA Recruiting:- EMPLOYMENT AND SALARY STATISTICS AT TOP B-SCHOOLS IN THE US! (2018)
MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!
The MOST AFFORDABLE MBA programs!
STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)
AVERAGE GRE Scores At The Top Business Schools!
Signature Read More
avatar
G
Shiv2016
Director
Director
Joined: 02 Sep 2016
Posts: 528
Re: If a is divisible by 6!, then a/5 must be [#permalink] New post  18 Apr 2017, 07:13
1
Kudos
a is divisible by 6!
i.e. a is divisible by 1*2*3*4*5*6


So least value of a is 6!= 1*2*3*4*5*6

a/5= 1*2*3*4*6

a has at least 2 prime nos. (2 and 3). So a is not a prime no.

As a has 3 as its prime factor, it is divisible by 3.

We just eliminated 5 and we are not sure if there is any other 5 or a multiple of 5 in the factors of a. So choice 3 is also not true as this is a MUST BE question.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18738
Location: United States (CA)
Re: If a is divisible by 6!, then a/5 must be [#permalink] New post  24 Apr 2017, 16:54
Expert Reply
Bunuel wrote:
If a is divisible by 6!, then a/5 must be

I. a prime number
II. divisible by 3
III. a multiple of 5

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III


Since 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720, we see that a = 720k for some positive integer k, and hence a/5 = 720k/5 = 144k.

Furthermore, since 144 is a multiple of 3, 144k will be always divisible by 3 for all values of k. However, since 144 is not a multiple of 5, 144k will only be a multiple of 5 for some values of k. Last but not least, since 144 is not a prime number, 144k will never be a prime number for any values of k.

Answer: B
_________________
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
Signature Read More
User avatar
B
Cez005
Manager
Manager
Joined: 13 Dec 2013
Posts: 102
Location: United States (NY)
Concentration: General Management, International Business
Schools: Cambridge"19 (A)
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE:Consulting (Consulting)
Reviews Badge
Re: If a is divisible by 6!, then a/5 must be [#permalink] New post  25 Apr 2017, 13:09
If a is divisible by 6!, the lowest value of is 6!. a/5 removes a factor of 5.
So, if a=6x5x4x3x2, then a/5 is not divisible by 5. In addition, it's clear that a/5 is not a prime.
Lastly, dividing by 5 does not remove the factor of 3. So we know that II is true.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92747
CAT Tests Forum Quiz Mode
Re: If a is divisible by 6!, then a/5 must be [#permalink] New post  03 Dec 2017, 08:22
Expert Reply
Bunuel wrote:
If a is divisible by 6!, then a/5 must be

I. a prime number
II. divisible by 3
III. a multiple of 5

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III


Similar questions:
https://gmatclub.com/forum/if-a-is-divi ... 30646.html
https://gmatclub.com/forum/if-a-is-divi ... 30155.html
https://gmatclub.com/forum/if-a-is-divi ... 30595.html
https://gmatclub.com/forum/if-a-is-divi ... 29901.html
https://gmatclub.com/forum/if-a-is-divi ... 28285.html
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
P
MHIKER
Director
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 972
Re: If a is divisible by 6!, then a/5 must be [#permalink] New post  12 Nov 2020, 00:59
Top Contributor
Bunuel wrote:
If a is divisible by 6!, then a/5 must be

I. a prime number
II. divisible by 3
III. a multiple of 5

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III


a is multiple of 6!
6!=6*5*4*3*2*1/5 IS NOT A PRIME NUMBER BECAUSE THE RESULT IS MULTIPLIED BY 2, SO IT'S A EVEN NUMBER (I) IS OUT.

II. 6*5*4*3*2*1/5 = 6*4*3*2*1 IS DIVIDED BY 3; TRUE

III. 6*5*4*3*2*1/5 = 6*4*3*2*1=144 IS NOT MULTIPLE OF 5

THE ANSWER IS B.
GMAT Club Bot
gmatclubot
Re: If a is divisible by 6!, then a/5 must be [#permalink]
12 Nov 2020, 00:59
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
92747 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions