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

It is currently 22 Feb 2020, 00:53

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

X is the product of integers from 1 to 50, inclusive. If 12^N is a fac

  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: 61385
X is the product of integers from 1 to 50, inclusive. If 12^N is a fac  [#permalink]

Show Tags

New post 09 Dec 2019, 01:13
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:51) correct 42% (01:46) wrong based on 57 sessions

HideShow timer Statistics

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3265
Location: India
GPA: 3.12
X is the product of integers from 1 to 50, inclusive. If 12^N is a fac  [#permalink]

Show Tags

New post 09 Dec 2019, 01:33
4
The formula for finding the highest power of a prime number in a factorial

If p is a prime number, then the highest power of p in a factorial n is {\(\frac{n}{p}\)} + {\(\frac{n}{p^2}\)} + {\(\frac{n}{p^3}\)}.....
where {\(\frac{a}{b}\)} is the quotient when integer b divides another integer a

Now coming to the problem at hand.

n = \(50\)
p = \(12 = 2^2*3\)

To find the highest power of 12, we need to find the highest power of 3(which is the bigger prime number)
Here, the bigger the prime number the lower will the frequency of that prime be in the factorial.

Therefore, the highest power of 12 in 50 is \({\frac{50}{3}} + {\frac{50}{3^2}} + {\frac{50}{3^3}} = 16 + 5 + 1 = 22\)(Option C)
_________________
You've got what it takes, but it will take everything you've got
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1224
Location: United States
CAT Tests
X is the product of integers from 1 to 50, inclusive. If 12^N is a fac  [#permalink]

Show Tags

New post 11 Dec 2019, 05:39
1
Bunuel wrote:
X is the product of integers from 1 to 50, inclusive. If 12^N is a factor of X, what is the greatest possible value of N?

A. 4
B. 12
C. 22
D. 28
E. 57


\(50!/{12}^n=50!/(2^23)^n\)
\(quotients(50/[2^1,2^2,2^3…2^x])=25+12+6+3=46\)
\(quotients(50/[3^1,3^2,3^3…3^x])=16+5+1=22\)
\(50!/(12)^n=(2^23)^n=(2^{2n}*3^n)=2^{2(22)}*3^{22}=(12)^{22}\)

Ans (C)
GMAT Club Bot
X is the product of integers from 1 to 50, inclusive. If 12^N is a fac   [#permalink] 11 Dec 2019, 05:39
Display posts from previous: Sort by

X is the product of integers from 1 to 50, inclusive. If 12^N is a fac

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





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