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

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Director
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V
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]

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New post 23 Mar 2019, 08:35
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

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

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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
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Joined: 11 Feb 2013
Posts: 149
Location: Bangladesh
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
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Re: What is the greatest integer that will divide both 5!/2! and 15!/13!?  [#permalink]

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New post 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.

So, my answer is C

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

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New post 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
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What is the greatest integer that will divide both 5!/2! and 15!/13!?   [#permalink] 25 Mar 2019, 13:33
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What is the greatest integer that will divide both 5!/2! and 15!/13!?

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