Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59182

What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:00
Question Stats:
30% (01:15) correct 70% (01:23) wrong based on 290 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Director
Joined: 28 Jul 2016
Posts: 654
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:22
(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.
Using statement 1 The value of 9 will account for all 3 that formed groups of 2 such as 3 *3 hence highest value will be 9*2 =18. But there can be some 3 which does not form a pair hence it could b 19 also. Thus not sufficient.
Using statement 2 highest power of 6 = 2*3 for every 3 there will be a corresponding 2 hence the highest power of 3 will be same as highest power of 6 = 19 Thus B is sufficient
Answer B




Manager
Joined: 30 May 2019
Posts: 109

What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
Updated on: 06 Jul 2019, 04:51
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.
From St 1 we just know that 9 is the highest power 9 in x!. So we can have either 18 or 19 units of 3 in x!. For example, I have tried 39! or 42!. In both cases, we have 9 in power of or 9^9. Thus not sufficient
We are told that highest power of 6 in the value of x! is 19. Since we get more 2s than 3s, power of 6 in x! is determined by number of 3s in x!. So, \(\frac{x!}{3}\)+\(\frac{x!}{3^2}\)+\(\frac{x!}{3^3}\)=19. Value 42! fits So x! is 42!, from here we can count number of 3. Hence, St 2 is sufficient Our answer B
Originally posted by mira93 on 05 Jul 2019, 08:13.
Last edited by mira93 on 06 Jul 2019, 04:51, edited 4 times in total.



Senior Manager
Joined: 12 Dec 2015
Posts: 439

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:17
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



Senior Manager
Joined: 10 Aug 2018
Posts: 339
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:22
The answer is B. Because as per A 3 can be 18 and 19. in both cases we will get 9 9's. As per B 3 is 19 only, Hence B is sufficient.
_________________
On the way to get into the Bschool and I will not leave it until I win. WHATEVER IT TAKES. " I CAN AND I WILL"
GMAT:[640 Q44, V34, IR4, AWA5]



Manager
Joined: 27 May 2010
Posts: 199

What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
Updated on: 06 Jul 2019, 01:19
Statement 1: Highest power of 9 is 9. Which implies highest power of 3 could be 18 or 19. Statement 2: Highest power of 6 is 19. This implies the highest power of 2 and 3 together is 19. However we don't know the highest power of 3. Combining both statemens together, the highest power of 3 has to be 19. Both statements together are required. Option C. Posted from my mobile device
_________________
Please give Kudos if you like the post
Originally posted by prashanths on 05 Jul 2019, 08:23.
Last edited by prashanths on 06 Jul 2019, 01:19, edited 1 time in total.



Manager
Joined: 15 Jun 2019
Posts: 210

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:25
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
_________________
please do correct my mistakes that itself a big kudo for me,
thanks



Manager
Joined: 29 Nov 2018
Posts: 148
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:28
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.



ISB School Moderator
Joined: 08 Dec 2013
Posts: 607
Location: India
Concentration: Nonprofit, Sustainability
WE: Operations (NonProfit and Government)

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:30
What is the highest power of 3 in the value of x!, where x is a positive integer? B, Statement# 2 only. (1) The highest power of 9 in the value of x! is 9. Let's see with powers of 2, In 8! highest power of 2 is 7, but highest power of 4 is 3. So not every time highest power of x^2 is twice that of highest power in x for a given factorial y!. Insufficient. (2) The highest power of 6 in the value of x! is 19. In 6 the only power of 3 is 1. So Highest power of 3 will also be 19.
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.GMAT Math Book I never wanted what I gave up I never gave up what I wanted



Manager
Joined: 04 Apr 2015
Posts: 235

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:30
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



Senior Manager
Joined: 31 May 2018
Posts: 451
Location: United States
Concentration: Finance, Marketing

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:32
STATEMENT (1) The highest power of 9 in the value of x! is 9. that means x! is divisible by \(9^9\) \(\frac{x!}{9^9}\) = x!/(3^2)^9
=x!/3^18 x! is divisible by 3^18 and 18 is the highest power of 3 in x! so SUFFICIENT
STATEMENT (2) The highest power of 6 in the value of x! is 19. that means x! is divisible by 6^19 x!/6^19 = x!/(2*3)^19
x!/2^19*3^19 x! is divisible by 3^19 and 19 is the highest power of 3 in x! so SUFFICIENT
D is the answer



Manager
Joined: 18 Jun 2013
Posts: 133
Location: India
Concentration: Technology, General Management
GPA: 3.2
WE: Information Technology (Consulting)

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:33
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.



Manager
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:38
1. 9 = \(3^2\) (We should factor it in primes.) that means we can use the formula:
If p is a prime number so the highest power of p^a in factorial n is given by: => (highest power of p in n!)/(a) => (highest power of 3 in x!)/(2) we can use the formula: =>\(\frac{(x)}{(3)}\) + \(\frac{(x)}{(3^2)}\)+ ... = 9
Sufficient.
2. 6 = 2*3 The 3 will have less power than 2 in x!. So, we can use the formula: => \(\frac{(x)}{(3)}\) + \(\frac{(x)}{(3^2)}\)+ ... = 19 We can find the X. Sufficient.
IMO the answer is D.
Please hit kudos if you like the solution.



BSchool Moderator
Joined: 07 Dec 2018
Posts: 144
Location: India

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:42
We are asked to find the HIGHEST power of 3 in x!
Statement 1 : The highest power of 9 in the value of x! is 9.
9 = 3^2
This is sufficient. Because 9 only consists of 3s.
Statement 2 : The highest power of 6 in the value of x! is 19.
6 = 3*2
This is NOT sufficient. All we can say is that x has a minimum of 19 3s. But 3s can be more. For example, if we have 19 2s and 20 3s, ONLY 19 6s are possible.
Having said that, I can't come up with a number right now, where this can be a scenario. But on the above reasoning, I'm ruling out statement 2.
So, Ans should be (A)



VP
Joined: 20 Jul 2017
Posts: 1089
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:45
(1) The highest power of 9 in the value of x! is 9. > x! = 9^9*k Here, k can be a multiple of 3 or a nonmultiple of 3 If k is a multiple of 3, k = 3m > x! = 9^9*3m = 3^18*3m = 3^19m > Highest Power of 3 = 19 If k is a non multiple of 3, x! = 9^9*k = 3^18*k > Highest Power of 3 = 18
Insufficient
(2) The highest power of 6 in the value of x! is 19. > x! = 6^19*p > x! = (2*3)^19*p > Highest Power of 3 = 19
Sufficient
IMO Option B
Pls Hit Kudos if you like the solution



Director
Joined: 22 Nov 2018
Posts: 562
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:49
(1) The highest power of 9 in the value of x! is 9.  Given that X!/3^2 is 9. Insufficient as the number of 3's can be 9*2=18 or 19 As you can have one more multiple of 3 which will not provide a 9 in X!. (2) The highest power of 6 in the value of x! is 19. = Since the prime factorization of 6 will have 3 has the highest prime (limiting factor of arriving at 6, as 2's will be more common than 3's.)directly provides the number of 3's  19. IMO B
_________________
Give +1 kudos if this answer helps..!!



Intern
Joined: 29 May 2019
Posts: 32

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:49
D each one is sufficient A as 3^2 =9 is sufficient to answer B as 2*3=6 is also sufficient to find the power of 3
Posted from my mobile device



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5305
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
Updated on: 06 Jul 2019, 12:49
IMO B
#1 The highest power of 9 in the value of x! is 9. 3^18 or 19 possible insufficient #2The highest power of 6 in the value of x! is 19 or say 2^19*3^19 ; highest power of 3 is 19 sufficient IMO B
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.
Originally posted by Archit3110 on 05 Jul 2019, 08:51.
Last edited by Archit3110 on 06 Jul 2019, 12:49, edited 1 time in total.



SVP
Joined: 03 Jun 2019
Posts: 1853
Location: India

What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
Updated on: 05 Jul 2019, 09:12
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. If the highest power of 9 in the value of x! is 9 then 9^9 is a factor of x! and so 3^18 is also a factor But no conclusion may be drawn about highest power of 3 since it may be 18 or 19. INSUFFICIENT. (2) The highest power of 6 in the value of x! is 19. If the higher power of 6 in x! is 19 then highest power of 3 in x! is also 19. Since highest power of 2 is always larger than higher power of 3 in x!. SUFFICIENT. Statement 2 alone is sufficient. IMO B
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources:  Efficient LearningAll you need to know about GMAT quantTele: +911140396815 Mobile : +919910661622 Email : kinshook.chaturvedi@gmail.com
Originally posted by Kinshook on 05 Jul 2019, 08:54.
Last edited by Kinshook on 05 Jul 2019, 09:12, edited 2 times in total.



Manager
Joined: 18 Sep 2018
Posts: 100

Re: What is the highest power of 3 in the value of X! ?
[#permalink]
Show Tags
05 Jul 2019, 08:57
IMO B
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.
St1: It says highest power of 9 is 9, that means highest power of 3 is 18. What if there is another 3 in the next few numbers, which we are missing here because that's not a factor of 9. (for e.g. 27 is a factor of 9, but 30 is not)
St2: It says highest power of 6 is 19, that means highest power of 3 is 19. There is no situation when a factor of 3 will appear and a factor of 2 will not appear. As factor of 3 is always followed by a factor of 3. (for e.g.  33 is followed by 32, 39 is followed by 38)




Re: What is the highest power of 3 in the value of X! ?
[#permalink]
05 Jul 2019, 08:57



Go to page
1 2 3 4
Next
[ 73 posts ]



