Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 Apr 2015, 17:57

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Intern
Joined: 06 Feb 2013
Posts: 11
Followers: 0

Kudos [?]: 13 [1] , given: 10

If a and b are positive integers, is a!/b! an integer? [#permalink]  20 Sep 2013, 13:01
1
KUDOS
00:00

Difficulty:

55% (hard)

Question Stats:

57% (02:27) correct 43% (01:28) wrong based on 82 sessions
If a and b are positive integers, is a!/b! an integer?

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

(2) b + a = 11
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27058
Followers: 4185

Kudos [?]: 40432 [4] , given: 5421

Re: If a and b are positive integers, is a!/b! an integer? [#permalink]  20 Sep 2013, 13:08
4
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

P.S. Please name the topics properly. Pay attention to rule #3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
_________________
Manager
Joined: 25 Oct 2013
Posts: 173
Followers: 0

Kudos [?]: 30 [0], given: 56

Re: If a and b are positive integers, is a!/b! an integer? [#permalink]  08 Feb 2014, 02:15
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.

_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Manager
Joined: 21 Oct 2013
Posts: 194
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Followers: 0

Kudos [?]: 18 [0], given: 19

Re: If a and b are positive integers, is a!/b! an integer? [#permalink]  05 Aug 2014, 03:11
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.

A.
Re: If a and b are positive integers, is a!/b! an integer?   [#permalink] 05 Aug 2014, 03:11
Similar topics Replies Last post
Similar
Topics:
4 If a and b are positive integers, is √(a+b) an integer? 5 16 Feb 2015, 05:56
17 If a and b are positive integers such that a-b and a/b are 13 25 Nov 2008, 05:00
If A and B are positive integers such that A-B and A/B are 3 25 Jan 2008, 10:03
If a and b are positive integers such that a-b and a/b are 5 26 Jul 2007, 13:38
If a and b are positive integers such that a-b and a/b 6 04 Jul 2005, 02:34
Display posts from previous: Sort by

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

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.