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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If a is divisible by 6!, then a/5 must be [#permalink]

Show Tags

18 Apr 2017, 04:42

1

This post received KUDOS

1

This post was BOOKMARKED

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.

Re: If a is divisible by 6!, then a/5 must be [#permalink]

Show Tags

18 Apr 2017, 06:13

1

This post received 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.
_________________

Help me make my explanation better by providing a logical feedback.

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
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: If a is divisible by 6!, then a/5 must be [#permalink]

Show Tags

25 Apr 2017, 12:09

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.