Last visit was: 11 Dec 2024, 07:33 It is currently 11 Dec 2024, 07:33
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Dec 2024
Posts: 97,807
Own Kudos:
685,048
 [22]
Given Kudos: 88,240
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,807
Kudos: 685,048
 [22]
If 12!/3^x is an integer, what is the greatest possible value of x? 28 Feb 2016, 09:13
Kudos
Add Kudos
22
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

81% (00:44) correct 19% (01:17) wrong based on 543 sessions

History

Date
Time
Result
Not Attempted Yet
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7
ShowHide Answer
Official Answer
C
Most Helpful Reply
avatar
sameerspice
avatar
Joined: 16 Apr 2015
Last visit: 31 Jul 2020
Posts: 24
Own Kudos:
125
 [5]
Given Kudos: 132
Posts: 24
Kudos: 125
 [5]
If 12!/3^x is an integer, what is the greatest possible value of x? 28 Feb 2016, 16:18
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7

This question is asking how many power of 3 exists in 12!
easiest way is to identify factor of three
12 -> 4*3 => 1 power of 3
9 -> 3*3=> 2 power of 3
6 -> 2*3=> 1 power of 3
3 -> 1*3=> 1 power of 3
Total equal 5 hence C
General Discussion
User avatar
sowragu
User avatar
Joined: 25 Dec 2012
Last visit: 26 Apr 2016
Posts: 104
Own Kudos:
122
 [1]
Given Kudos: 148
Posts: 104
Kudos: 122
 [1]
If 12!/3^x is an integer, what is the greatest possible value of x? 28 Feb 2016, 13:19
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7

12 - 4*3
9 - 3*3
6 - 2*3
3 - 1*3

Hence max of 3^5 is allowed. IMO C.

This is not the right way of doing. Forgot the easy approach. Will update.
User avatar
law258
User avatar
Joined: 05 Sep 2016
Last visit: 11 Oct 2020
Posts: 264
Own Kudos:
107
 [1]
Given Kudos: 283
Status:DONE!
Posts: 264
Kudos: 107
 [1]
If 12!/3^x is an integer, what is the greatest possible value of x? 29 Oct 2016, 08:52
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
12/3 + 12/9 = 4 + 1 = 5

3^5
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 02 Oct 2024
Posts: 6,014
Own Kudos:
4,946
 [2]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 6,014
Kudos: 4,946
 [2]
If 12!/3^x is an integer, what is the greatest possible value of x? 29 Oct 2016, 11:32
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7

12/3 = 4
4/3 = 1

4 + 1 = 5

Hence correct answer will be (C) 5
avatar
ankurkshl
avatar
Joined: 26 Feb 2017
Last visit: 14 Jul 2018
Posts: 2
Given Kudos: 62
Posts: 2
Kudos: 0
If 12!/3^x is an integer, what is the greatest possible value of x? 27 Jun 2018, 08:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Abhishek009
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7

12/3 = 4
4/3 = 1

4 + 1 = 5

Hence correct answer will be (C) 5

i didnt understand why you divided 4 by 3.
please explain
User avatar
gmatzpractice
User avatar
Joined: 07 Feb 2017
Last visit: 25 Nov 2024
Posts: 128
Own Kudos:
64
Given Kudos: 11
GMAT 1: 710 Q48 V40
GMAT 1: 710 Q48 V40
Posts: 128
Kudos: 64
If 12!/3^x is an integer, what is the greatest possible value of x? 27 Jun 2018, 11:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
12=3*4
9=3*3
6=3*2
3

Answer C. count of 3 s
avatar
ankurkshl
avatar
Joined: 26 Feb 2017
Last visit: 14 Jul 2018
Posts: 2
Given Kudos: 62
Posts: 2
Kudos: 0
If 12!/3^x is an integer, what is the greatest possible value of x? 28 Jun 2018, 16:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Abhishek009
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7

12/3 = 4
4/3 = 1

4 + 1 = 5

Hence correct answer will be (C) 5

Kindly specify dividing 4 by 3 by the same shortcut method that you have applied in the tagged answer.
i have got the factorisation concept.

thanks.

regards.
User avatar
generis
User avatar
Senior SC Moderator
Joined: 22 May 2016
Last visit: 18 Jun 2022
Posts: 5,316
Own Kudos:
36,309
 [2]
Given Kudos: 9,464
Products:
GMAT Club Tests
Expert reply
Posts: 5,316
Kudos: 36,309
 [2]
If 12!/3^x is an integer, what is the greatest possible value of x? 30 Jun 2018, 14:16
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7
This question is easy, and a good way to demonstrate one way to find the number of "powers of a prime in \(n!\)." (See footnote.*)

This \(n!\) is small. Most will not be.

The method: Divide \(n=12\) (without !) by increasing powers of \(3\). Don't worry about remainders.

(1) 12 divided by \(3^1:(\frac{12}{3^1})=4\)

(2) 12 divided by \(3^2: (\frac{12}{3^2})=(\frac{12}{9})=1\)

(3) 12 divided by \(3^3=27\):
Will not work. \(\frac{12}{27}<1\)

(4) Add up the results of division by each power of 3 that "worked": \((4 + 1) = 5\)

There are 5 powers of 3 in 12!, so the greatest possible value of \(x=5\)

Answer C

*The theory is described by Bunuel in Everything About Factorials, Finding the Number of Powers of a Prime, p, in the n!, here. Important! The post also has an example.
User avatar
generis
User avatar
Senior SC Moderator
Joined: 22 May 2016
Last visit: 18 Jun 2022
Posts: 5,316
Own Kudos:
36,309
 [3]
Given Kudos: 9,464
Products:
GMAT Club Tests
Expert reply
Posts: 5,316
Kudos: 36,309
 [3]
If 12!/3^x is an integer, what is the greatest possible value of x? 30 Jun 2018, 14:16
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ankurkshl
Abhishek009
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7
12/3 = 4
4/3 = 1

4 + 1 = 5

Hence correct answer will be (C) 5
Kindly specify dividing 4 by 3 by the same shortcut method that you have applied in the tagged answer.
i have got the factorisation concept.

thanks.

regards.
ankurkshl , the method is one way to find the number of powers of a prime number in \(n!\).
Divide \(n\) (without the !) by the prime number (here, 3). \(n=12\)

Use the resulting quotient as your new dividend, and divide again by \(3\) until the resulting number is too small to divide by \(3\)

1) 12 divided by 3: \(\frac{12}{3^1}=4\)

2) Now use \(4\), and divide by 3. Do not worry about remainders.* \(\frac{4}{3}=1\)

3) Sum the number of 3s from all stages:
(4 + 1) = 5

There are five factors of 3 in 12!, so the greatest possible value for x is 5.

Answer C

Hope that helps. :-)

*We just need to know whether \(4\) can be divided by \(3\) such that the result \(\geq1\)
(How many times does 3 go into 4? One time, with a remainder about which we do not care). This method is a variation on the method I posted above. Both are VERY handy when n! is huge.
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 3,023
Own Kudos:
7,202
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert reply
Posts: 3,023
Kudos: 7,202
If 12!/3^x is an integer, what is the greatest possible value of x? 02 Jul 2018, 10:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7

o determine the number of factors of 3 within 12!, we can use the following shortcut in which we divide 12 by 3, and then divide the quotient of 12/3 by 3 and continue this process until we can no longer get a nonzero integer as the quotient.

12/3 = 4

4/3 = 1 (we can ignore the remainder)

Since 1/3 does not produce a nonzero quotient, we can stop.

The final step is to add up our quotients; that sum represents the number of factors of 3 within 12!.

Thus, there are 4 + 1 = 5 factors of 3 within 12!. Thus, the greatest value of x is 5.

Answer: C
User avatar
Kinshook
User avatar
GMAT Club Legend
Joined: 03 Jun 2019
Last visit: 11 Dec 2024
Posts: 5,422
Own Kudos:
4,593
Given Kudos: 161
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
Posts: 5,422
Kudos: 4,593
If 12!/3^x is an integer, what is the greatest possible value of x? 09 Jul 2020, 11:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7

Asked: If 12!/3^x is an integer, what is the greatest possible value of x?

Max power of 3 in 12! = [12/3] + [12/3^2] = 4 + 1 = 5

IMO C
avatar
QQRamanQQ
avatar
Joined: 29 Apr 2016
Last visit: 08 Jun 2023
Posts: 74
Own Kudos:
14
Given Kudos: 30
Location: India
GPA: 3
Posts: 74
Kudos: 14
If 12!/3^x is an integer, what is the greatest possible value of x? 06 Sep 2020, 06:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why didn't we include 3^0 in the option? question doesn't specify there cant be zero. Can anyone help me with this one? if we include 3^0, we get D as the correct answer. Can anyone help me with this?
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 02 Oct 2024
Posts: 6,014
Own Kudos:
4,946
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 6,014
Kudos: 4,946
If 12!/3^x is an integer, what is the greatest possible value of x? 06 Apr 2022, 09:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If 12!/3^x is an integer, what is the greatest possible value of x?

A. 3
B. 4
C. 5
D. 6
E. 7
12/3 = 4
4/3 = 1

So, Highest power of x is 4 + 1 = 5 , Answer will be (C)
Moderator:
Bunuel
Math Expert
97806 posts