Last visit was: 19 Jul 2024, 05:05 It is currently 19 Jul 2024, 05:05
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94411
Own Kudos [?]: 642237 [33]
Given Kudos: 86282
Send PM
Most Helpful Reply
VP
VP
Joined: 28 Jul 2016
Posts: 1199
Own Kudos [?]: 1751 [6]
Given Kudos: 67
Location: India
Concentration: Finance, Human Resources
Schools: ISB '18 (D)
GPA: 3.97
WE:Project Management (Investment Banking)
Send PM
General Discussion
Current Student
Joined: 30 May 2019
Posts: 118
Own Kudos [?]: 254 [4]
Given Kudos: 1696
Location: Tajikistan
Concentration: Finance, General Management
Schools: Simon '24 (A)
GMAT 1: 610 Q46 V28
GMAT 2: 730 Q49 V40 (Online)
GPA: 3.37
WE:Analyst (Consulting)
Send PM
Senior Manager
Senior Manager
Joined: 12 Dec 2015
Posts: 464
Own Kudos [?]: 546 [2]
Given Kudos: 84
Send PM
Re: What is the highest power of 3 in the value of X! ? [#permalink]
1
Kudos
1
Bookmarks
What is the highest power of 3 in the value of x!, where x is a positive integer?

(1) The highest power of 9 in the value of x! is 9. --> not correct: x! = 9^9 *k = 3^18*k(k is an integer, not multiple of 9, but can be or can't be multiple of 3) where k can be or can't be multiple of 3, so the highest power of 3 can be 18 or 19
(2) The highest power of 6 in the value of x! is 19. --> correct: x! = 6^19*m(m is an integer, not multiple of 3) = 3^19*n, so the highest power of 3 must be 19

Answer: B
Manager
Manager
Joined: 15 Jun 2019
Posts: 134
Own Kudos [?]: 217 [2]
Given Kudos: 123
Send PM
Re: What is the highest power of 3 in the value of X! ? [#permalink]
2
Kudos
imo option B,

condition a, signifies 9 ^9, which says 3^18 or 3^19 both can be answers

condtion b, says 6^19, which is equivalent to 3^19 as no of 2 will be definitely more than 19, to form 6^19
Manager
Manager
Joined: 29 Nov 2018
Posts: 93
Own Kudos [?]: 186 [3]
Given Kudos: 57
Location: India
Concentration: Entrepreneurship, General Management
GMAT 1: 730 Q50 V40
GPA: 3.99
WE:Engineering (Computer Hardware)
Send PM
Re: What is the highest power of 3 in the value of X! ? [#permalink]
3
Kudos
What is the highest power of 3 in the value of x!, where x is a positive integer?

(1) The highest power of 9 in the value of x! is 9.
(2) The highest power of 6 in the value of x! is 19.

Answer is B
The power of 6 always indicates power of 3 as power of 2 will always be more than power of 3.

For eg: if x=9 then in 9! the highest power of 2 is 7 but highest power of 3 is 4. so highest power of 6 will be 4 which is same as highest power of 3.
Manager
Manager
Joined: 04 Apr 2015
Posts: 231
Own Kudos [?]: 137 [2]
Given Kudos: 269
GMAT 1: 650 Q49 V31
GPA: 3.59
Send PM
Re: What is the highest power of 3 in the value of X! ? [#permalink]
1
Kudos
1
Bookmarks
we know that for the power 3 in x factorial we need to count all 3 present in X!

statement 1 : we know the power of 9 in x! but there could be a 3 that couldn't form a pair to be 9 and was not counted so insufficient
statement 2 : we know the power of 6 in x! therefore we have already accounted for all the 3 as for any factorial we will see the number of 2 in the factorial will be greater than the number 3 so all 3's have formed pair .therefore sufficient

answer B
Manager
Manager
Joined: 18 Jun 2013
Posts: 86
Own Kudos [?]: 193 [3]
Given Kudos: 198
Location: India
Concentration: Technology, General Management
GMAT 1: 690 Q50 V35
GPA: 3.2
WE:Information Technology (Consulting)
Send PM
Re: What is the highest power of 3 in the value of X! ? [#permalink]
2
Kudos
1
Bookmarks
What is the highest power of 3 in the value of x!, where x is a positive integer?

Option 1: The highest power of 9 in the value of x! is 9.

Now in option 1 let us consider 2 possibilities,

1 - Can the highest power of 9 give us the highest power of 3s in x!? - Maybe. If yes, then 9^9 = 3^18 => highest power of 3 being 18 --> this is possible.
2 - Can the highest power of 9 not give us the highest power of 3s in x!? - Maybe. If yes, then we will have atleast 1 more 3 which will ensure highest power of 9 remains 9 and that highest power of 3 is not 18 but rather 19. Imagine this like 9^9 * 3 being a part of the x!.

Hence since both above considered cases are possible, option 1 is not sufficient.

Option 2: The highest power of 6 in the value of x! is 19.

6^19 = 2^19 x 3^19

Now in option 2 let us consider 2 possibilities,

1 - Can the highest power of 6 give us the highest power of 3s in x!? - Yes. Highest power of 6 will always contain the highest power of 3 as every 3 will havea corresponding 2 to form 6 (vice versa may not be true).
2 - Can the highest power of 6 not give us the highest power of 3s in x!? - No. There cannot be a case where we have highest power of 6 in x! and also an extra 3 which does not have a corresponding 2 available to form a 6.

Hence, since both above considered cases are in synch, option 2 is sufficient.
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13808 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: What is the highest power of 3 in the value of X! ? [#permalink]
1
Kudos
Expert Reply
Quote:
What is the highest power of 3 in the value of x!, where x is a positive integer?

(1) The highest power of 9 in the value of x! is 9.
(2) The highest power of 6 in the value of x! is 19.


The highest power of 3 in x! depends on value of x

Statement 1: Power of 9 in x! is 9

but power of 3 in x! may be 18 or 19 hence
NOT SUFFICIENT

Statement 2: Power of 6 in x! = 19
but each 6 is made of one 2 and one 3
Powers of 2 will be higher than power of 3 in any factorial so power of 6 will be as many as the power of 3
hence, power of 3 in x! = 19
SUFFICIENT

Answer: Option B
Manager
Manager
Joined: 08 Jan 2018
Posts: 73
Own Kudos [?]: 239 [1]
Given Kudos: 374
Send PM
Re: What is the highest power of 3 in the value of X! ? [#permalink]
1
Kudos
We are required to find the highest power of 3 in x!

(1) The highest power of 9 in the value of x! is 9.

Consider 9!
The highest power of 3 in 9! is = Quotient of (\(\frac{9}{3}\)) + Quotient of (\(\frac{9}{3^2}\)) = 3 + 1 = 4
Thus, the number of 9s i.e \(3^2\) that can be formed is 2
So the highest power of 9 in 9! is 2
Thus in this case, highest power of 3 = 2 * Highest power of 9

Consider 12!
The highest power of 3 in 12! Is = Quotient of (\(\frac{12}{3}\)) + Quotient of (\(\frac{12}{3^2}\)) = 4 + 1 = 5
Thus, the number of 9s i.e \(3^2\) that can be formed is 2 (using four 3s out of five)
So the highest power of 9 in 12! is 2
Thus in this case, highest power of 3 NOT EQUAL to 2 * Highest power of 9

Therefore, we cannot be sure of the highest power of 3 in a factorial by knowing highest power of 9.

Not Sufficient.

(2) The highest power of 6 in the value of x! is 19.
6 is a composite number so the highest power of 6 in a factorial will depend upon the number of pairs of 2 and 3 that can be formed in the factorial.

Consider 9!
The highest power of 2 in 9! Is = Quotient of (\(\frac{9}{2}\)) + Quotient of (\(\frac{9}{2^2}\)) + Quotient of (\(\frac{9}{2^3}\)) = 4 + 2 + 1 = 7
The highest power of 3 in 9! Is = Quotient of (\(\frac{9}{3}\)) + Quotient of (\(\frac{9}{3^2}\)) = 4 + 1 = 5
The maximum number of 6s (2 * 3)s that can be formed by taking Seven 2s and Five 3s is 5
Therefore, the highest power of 6 in 9! = 5 = Highest power of 3 in 9!

Consider 12!
The highest power of 2 in 12! Is = Quotient of (\(\frac{12}{2}\)) + Quotient of (\(\frac{12}{2^2}\)) + Quotient of (\(\frac{12}{2^3}\)) = 6 + 3 + 1 = 10
The highest power of 3 in 12! Is = Quotient of (\(\frac{12}{3}\)) + Quotient of (\(\frac{12}{3^2}\)) = 4 + 1 = 5
Thus, the number of 6s that can be formed = 5
Therefore, the highest power of 6 in 12! = 5 = Highest power of 3 in 12!

Hence, in any factorial, the number of 2s will ALWAYS BE MORE than the number of 3s. So, the 2s can always pair up with all the 3s to form 6s. So highest power of 3 will always be equal to the highest power of 6

Sufficient.

Answer B
Manager
Manager
Joined: 28 May 2014
Posts: 65
Own Kudos [?]: 54 [0]
Given Kudos: 164
Location: Singapore
Concentration: Strategy
GMAT 1: 590 Q44 V27
Send PM
Re: What is the highest power of 3 in the value of X! ? [#permalink]
GMATinsight wrote:
Quote:
What is the highest power of 3 in the value of x!, where x is a positive integer?

(1) The highest power of 9 in the value of x! is 9.
(2) The highest power of 6 in the value of x! is 19.


The highest power of 3 in x! depends on value of x

Statement 1: Power of 9 in x! is 9

but power of 3 in x! may be 18 or 19 hence
NOT SUFFICIENT

Statement 2: Power of 6 in x! = 19
but each 6 is made of one 2 and one 3
Powers of 2 will be higher than power of 3 in any factorial so power of 6 will be as many as the power of 3
hence, power of 3 in x! = 19
SUFFICIENT

Answer: Option B


Can you please explain how the power of 3 in x! can be 19. I was only able to obtain 18.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34018
Own Kudos [?]: 852 [0]
Given Kudos: 0
Send PM
Re: What is the highest power of 3 in the value of X! ? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: What is the highest power of 3 in the value of X! ? [#permalink]
Moderator:
Math Expert
94411 posts