GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 22 Jan 2020, 06:21

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

If k and n are both integer and k > n > 0 is k!/n! divisible by 30 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60594
If k and n are both integer and k > n > 0 is k!/n! divisible by 30 ?  [#permalink]

Show Tags

New post 13 Nov 2019, 02:36
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

48% (02:08) correct 53% (01:45) wrong based on 40 sessions

HideShow timer Statistics

Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8341
Re: If k and n are both integer and k > n > 0 is k!/n! divisible by 30 ?  [#permalink]

Show Tags

New post 13 Nov 2019, 06:56
If k and n are both integer and \(k > n > 0\) is \(\frac{k!}{n!}\) divisible by 30 ?
\(\frac{k!}{n!}\) will surely be divisible by 30 if there are at least a difference of 5 between them as product of 5 consecutive numbers will be multiple of 2, 3 and 5 and hence 30...

(1) \(k + n = 30\)
\(k\neq{n}\), so the closest they will be when k=16 and n=14, so \(\frac{k!}{n!}\)=\(\frac{16!}{14!}=16*15=8*30\), hence divisible by 30.
Any further gap between k and n will surely have 15*16 in it..
Suff

(2) \(k - n = 6\)
this means consecutive six integers and their product will be at least 1*2*3*4*5*6, so divisible by 30.

D
_________________
GMAT Tutor
User avatar
S
Joined: 17 Sep 2014
Posts: 332
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
If k and n are both integer and k > n > 0 is k!/n! divisible by 30 ?  [#permalink]

Show Tags

New post 13 Nov 2019, 08:59
Bunuel wrote:
If k and n are both integer and \(k > n > 0\) is \(\frac{k!}{n!}\) divisible by 30 ?


(1) \(k + n = 30\)

(2) \(k - n = 6\)


Are You Up For the Challenge: 700 Level Questions


Analyzing the question:
30 = 2 * 3 * 5. We need a factor of 2, 3, and 5 from (k!/n!). If k and n have a difference of at least 5, we automatically get these factors from the numbers between k and n. For example, if k = 13 and n = 8, then we have k! / n! = 13 * 12 * 11 * 10 * 9 which is 5 numbers multiplied since k - n = 5. We can find a multiple of 5 for sure since there are 5 consecutive numbers multiplied, a multiple of 2 and 3 as well.

Statement 1:
If k and n are too far apart (k!/n!) will have a factor of 30 as demonstrated above. So let us focus on the closer k and n pairs, k = 16 and n = 14 -> (k!/n!) = 16 * 15. It has a factor of 30. If we take a bigger k we can see it will expand the factors for (k!/n!) so this is sufficient. (e.g. k = 17 n = 13, k!/n! = 17*16*15*14 which is more factors)

Statement2:
As demonstrated above, this is sufficient.

Ans: D
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
GMAT Club Bot
If k and n are both integer and k > n > 0 is k!/n! divisible by 30 ?   [#permalink] 13 Nov 2019, 08:59
Display posts from previous: Sort by

If k and n are both integer and k > n > 0 is k!/n! divisible by 30 ?

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne