NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 10:26 It is currently 23 Apr 2024, 10:26
Decision Tracker
My Rewards
New posts
New comers' posts

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

What is the greatest value of x such that 8^x is a factor of

User avatar
tarek99
Director
Director
Joined: 21 Jul 2006
Posts: 771
Own Kudos [?]: 4719 [0]
Given Kudos: 1
 Q49  V35
Send PM
What is the greatest value of x such that 8^x is a factor of [#permalink] New post   Updated on: 23 Oct 2008, 09:30
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Hide Show timer Statistics
1. What is the greatest value of \(x\) such that \(8^x\) is a factor of 16!?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8



2. What is the greatest value of q such that 9^q is a factor of 21! ?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6



Please show me the fastest way to approach this.

Thanks



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!

Originally posted by tarek99 on 17 Oct 2008, 07:27.
Last edited by tarek99 on 23 Oct 2008, 09:30, edited 1 time in total.
User avatar
LiveStronger
Manager
Manager
Joined: 21 Apr 2008
Posts: 114
Own Kudos [?]: 294 [0]
Given Kudos: 0
Location: Motortown
Send PM
Re: What is the greatest value of x such that 8^x is a factor of [#permalink] New post   17 Oct 2008, 13:05
C = 5

This is how approached it

8^x = 2^(3x)
From 16! pick all the number that can be divided by 2

16*8*4*2 = 2^10
and
14*12*10*6 = 2^5

so 2^(3x) = 2^15
x=5

I am sure there are formulae to solve it more easily, but this is what I could do :)
User avatar
rampuria
Manager
Manager
Joined: 04 Sep 2008
Posts: 149
Own Kudos [?]: 296 [0]
Given Kudos: 56
Location: Kolkata
Concentration: Strategic Management
Schools:La Martiniere for Boys
Send PM
Re: What is the greatest value of x such that 8^x is a factor of [#permalink] New post   21 Oct 2008, 06:02
Here's a better approach...

Combination of 4 and 2 will give a product of eight. So if we find the max. no. of pairs of 4 and 2 we can find the max. of x.

Now the no. of 4's that we can extract out of 16! is less than the the no. of 2's. In other words 2's are available in plenty in comparison to 4's. So our answer gets further restricted to the max. no.s of of 4's.

Now the no. of 4's is given by the 16/4 = 4 and 16/ 4^2 =1

therefore 5
User avatar
amitdgr
Director
Director
Joined: 30 Jun 2008
Posts: 538
Own Kudos [?]: 2727 [0]
Given Kudos: 1
Send PM
Re: What is the greatest value of x such that 8^x is a factor of [#permalink] New post   22 Oct 2008, 02:38
rampuria wrote:
Here's a better approach...

Combination of 4 and 2 will give a product of eight. So if we find the max. no. of pairs of 4 and 2 we can find the max. of x.

Now the no. of 4's that we can extract out of 16! is less than the the no. of 2's. In other words 2's are available in plenty in comparison to 4's. So our answer gets further restricted to the max. no.s of of 4's.

Now the no. of 4's is given by the 16/4 = 4 and 16/ 4^2 =1

therefore 5


Agreed :)
User avatar
icandy
Director
Director
Joined: 05 Jul 2008
Posts: 623
Own Kudos [?]: 1952 [0]
Given Kudos: 1
 Q49  V41
Send PM
Re: What is the greatest value of x such that 8^x is a factor of [#permalink] New post   22 Oct 2008, 09:32
My approach was to figure out how many 8's I can make out of 16!

16 = 8 X 2 14 = 2 X 7 and so on for all even numbers.

8 can also be arrived at by 2 ^ 3 or 4 X 2 ( such numbers are formed from left out of numbers of 14 , 12 etc)

we get 5 eights and hence x=5
User avatar
tarek99
Director
Director
Joined: 21 Jul 2006
Posts: 771
Own Kudos [?]: 4719 [0]
Given Kudos: 1
 Q49  V35
Send PM
Re: What is the greatest value of x such that 8^x is a factor of [#permalink] New post   22 Oct 2008, 16:48
rampuria wrote:
Here's a better approach...

Combination of 4 and 2 will give a product of eight. So if we find the max. no. of pairs of 4 and 2 we can find the max. of x.

Now the no. of 4's that we can extract out of 16! is less than the the no. of 2's. In other words 2's are available in plenty in comparison to 4's. So our answer gets further restricted to the max. no.s of of 4's.

Now the no. of 4's is given by the 16/4 = 4 and 16/ 4^2 =1

therefore 5


so according to your approach, how would you then solve this problem:



What is the greatest value of \(q\) such that \(9^q\) is a factor of 21! ?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
User avatar
kandyhot27
Intern
Intern
Joined: 03 Mar 2008
Posts: 16
Own Kudos [?]: 18 [0]
Given Kudos: 0
Send PM
Re: What is the greatest value of x such that 8^x is a factor of [#permalink] New post   22 Oct 2008, 19:28
LiveStronger wrote:
C - 4

3^8 = 3^2q
q = 4


for whatever reason i m getting 3^9 = 3^2q
Pls help me see why ?

3 6 9 12 15 18 21 = 3^9
1+1+2+1+1+2+1=9



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: What is the greatest value of x such that 8^x is a factor of [#permalink]
22 Oct 2008, 19:28
Moderators:
Bunuel
Math Expert
92875 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions