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:

If a and b are positive integers, is a!/b! an integer?

In order a!/b! to be an integer, a must be more than or equal to b. Thus the question basically asks whether \(a\geq{b}\).

(1) (b - a)(b + a) = 7! + 1 --> \(b^2-a^2=7! + 1=positive\). Since a and b are positive integers, then b>a. So, the answer to the question is NO. Sufficient.

(2) b + a = 11. We cannot determine whether \(a\geq{b}\). Not sufficient.

Re: If a and b are positive integers, is a!/b! an integer? [#permalink]

Show Tags

08 Feb 2014, 03:15

Given that a & b are both positive integers. For \(\frac{a!}{b!}\) to be integer a must be greater than or equal to b. otherwise a!/b! is going to be a fraction. We can then re-phrase the question to

Is a >= b?

Statement 1: (b-a)(b+a) = 7!+1. 7!+1 is +ve. b+a is +ve. b-a also has to be positive. note that b != a. then b>a. so a!/b! can not be integer. Sufficient.

Statement 2: a+b=11. a=1 b=10 ++> a!/b! is not integer. reverse the values, that is b=1, a=10 then yes. Since we have a yes and no. Insufficient.

Re: If a and b are positive integers, is a!/b! an integer? [#permalink]

Show Tags

05 Aug 2014, 04:11

From question: in order to a!/b! = integer, a has to be greater or equal to b. Hence the question becomes is a>=b?

(1) (b-a)(b+a) = 7! + 1 --> b²-a² = 7!+1. Since 7! + 1 is >0, b is > a (since both are positive integers) and the answer is NO. Suff. (2) b+a = 11, if b = 5 and a = 6 then answer is YES, if b = 6 and a = 5 answer is NO. IS.

Re: If a and b are positive integers, is a!/b! an integer? [#permalink]

Show Tags

05 Nov 2015, 21:46

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: If a and b are positive integers, is a!/b! an integer? [#permalink]

Show Tags

25 Feb 2016, 19:57

josemarioamaya wrote:

If a and b are positive integers, is a!/b! an integer?

(1) (b - a)(b + a) = 7! + 1

(2) b + a = 11

I rephrased the question to: is a greater or equal to b? otherwise, if b>, then a!/b! will not be an integer.

1 - b^2 - a^2 = 7!+1 so we know that both are positive integers, and b^2 is greater than a^2. it means that b is greater than a, and we know for sure that a!/b! is not an integer. B, C, and E - out.

2 - b+a=11. if a=6, b=5, then it is an integer if a=5, b=6, then not. B is out, so the answer is:

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

“Oh! Looks like your passport expires soon” – these were the first words at the airport in London I remember last Friday. Shocked that I might not be...