GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 21:59

### 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

# What is the greatest integer that will divide both 5!/2! and 15!/13!?

Author Message
Director
Joined: 18 Feb 2019
Posts: 581
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
What is the greatest integer that will divide both 5!/2! and 15!/13!?  [#permalink]

### Show Tags

23 Mar 2019, 08:35
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:21) correct 32% (01:18) wrong based on 47 sessions

### HideShow timer Statistics

For a positive integer n, n! denotes the product of all integers from 1 to n, inclusive. What is the greatest integer that will divide both 5!/2! and 15!/13!?

A. 1
B. 15
C. 30
D. 420
E. 840
Manager
Joined: 11 Feb 2013
Posts: 149
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: What is the greatest integer that will divide both 5!/2! and 15!/13!?  [#permalink]

### Show Tags

23 Mar 2019, 08:53
1
5!/2!=3*4*5=60
15!/13!=14*15=14*(10+5)=140+70=210

Now the question becomes what is the greatest number that divides 60 & 210 completely?

420 & 840 can't be factors of 60.
But, 30 can divide 60 & 210 completely.

Posted from my mobile device
Senior Manager
Joined: 12 Sep 2017
Posts: 302
What is the greatest integer that will divide both 5!/2! and 15!/13!?  [#permalink]

### Show Tags

25 Mar 2019, 13:33
What are we looking for? search for the 5's.

5! = 1
15! = 3
13! = 2

We are looking for a number that has at least 6 5's.

$$\frac{30!}{5!}=6$$

$$\frac{30!}{25!}=1$$

$$Total 5's = 7$$

C
What is the greatest integer that will divide both 5!/2! and 15!/13!?   [#permalink] 25 Mar 2019, 13:33
Display posts from previous: Sort by