Find all School-related info fast with the new School-Specific MBA Forum

It is currently 14 Jul 2014, 02:03

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the greatest value of m such that 4m is a factor of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 10 Oct 2005
Posts: 56
Followers: 1

Kudos [?]: 0 [0], given: 0

GMAT Tests User
What is the greatest value of m such that 4m is a factor of [#permalink] New post 25 Jun 2006, 17:11
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
What is the greatest value of m such that 4m is a factor of 30! ?

(A) 13
(B) 12
(C) 11
(D) 7
(E) 6
VP
VP
User avatar
Joined: 25 Nov 2004
Posts: 1499
Followers: 5

Kudos [?]: 22 [0], given: 0

GMAT Tests User
Re: PS : Exponents [#permalink] New post 25 Jun 2006, 18:10
briozeal wrote:
What is the greatest value of m such that 4m is a factor of 30! ?

(A) 13
(B) 12
(C) 11
(D) 7
(E) 6

i guess 4m=4^m.

go with A. 13.

2=30/2=15
4=30/4=7
8=30/8=3
16=30/16=1
total 2's = 26 i.e thirteen (13) 4's.
Manager
Manager
avatar
Joined: 09 Apr 2006
Posts: 173
Location: Somewhere in Wisconsin!
Followers: 1

Kudos [?]: 1 [0], given: 0

GMAT Tests User
 [#permalink] New post 25 Jun 2006, 20:50
Ans is 13 if the expression is 4^m. I don't think 4m is the right expression.
_________________

Thanks,
Zooroopa

Manager
Manager
avatar
Joined: 12 Apr 2006
Posts: 220
Location: India
Followers: 1

Kudos [?]: 18 [0], given: 17

GMAT Tests User
Re: PS : Exponents [#permalink] New post 25 Jun 2006, 23:08
MA wrote:
go with A. 13.

2=30/2=15
4=30/4=7
8=30/8=3
16=30/16=1
total 2's = 26 i.e thirteen (13) 4's.


I know I am dumb :oops: But I would be very thankful if somebody explain this a little bit more, as I wasn't able to get why we divided here only upto 16 or what exactly is logic behind this division.
VP
VP
User avatar
Joined: 25 Nov 2004
Posts: 1499
Followers: 5

Kudos [?]: 22 [0], given: 0

GMAT Tests User
Re: PS : Exponents [#permalink] New post 26 Jun 2006, 13:27
Quote:
What is the greatest value of m such that 4^m is a factor of 30! ?

(A) 13
(B) 12
(C) 11
(D) 7
(E) 6


4^m = 2^2m
30! = 1x2x3x4x5x6x7x8x9x10x......................x30.
if we count on factors of 30!, we have

1. 15 two's.
2. 7 four's.
3. 3 eight's
4. 1 sixteens.

this is because if we only count 2's, we ignore some other 2's. for ex: 4 has 2 two's. therefore, we do this procedure to find the number of 2's or 4's.

if we add all 2's, we have 26 two's (2's).
2^26 = 4^13.

i am not sure whether i explained it clearly. I will try again if any.

humans wrote:
MA wrote:
go with A. 13.

2=30/2=15
4=30/4=7
8=30/8=3
16=30/16=1
total 2's = 26 i.e thirteen (13) 4's.


I know I am dumb :oops: But I would be very thankful if somebody explain this a little bit more, as I wasn't able to get why we divided here only upto 16 or what exactly is logic behind this division.
Director
Director
User avatar
Joined: 28 Dec 2005
Posts: 761
Followers: 1

Kudos [?]: 8 [0], given: 0

GMAT Tests User
 [#permalink] New post 28 Jun 2006, 12:43
The answer is A. To break down any factorial into its prime factors, here is what you do:-

4^m = 2^2m

So we need to find the highest m for which 2^2m divides 30!.

30/2 = 15 (take only the quotient)
15/2 = 7 (take only the quotient)
7/2 = 3 (take only the quotient)
3/2 = 1 (take only the quotient)

When you get a quotient that is not divisible by the divisor or will give a fraction, stop. Add all the quotients, and you have the highest power of the number 2 that divides 30!. As you can see, this is 15 + 7 + 3 + 1 = 26.

Therefore 2m=26 or m=13.

Hope this helps.

Now if the question said 4m divides 30!, you just need to find the highest number that divides 30!/4, which is again 13.

Manager
Manager
User avatar
Joined: 19 Apr 2006
Posts: 231
Followers: 1

Kudos [?]: 1 [0], given: 0

GMAT Tests User
 [#permalink] New post 28 Jun 2006, 16:06
Futuristic wrote:
The answer is A. To break down any factorial into its prime factors, here is what you do:-

4^m = 2^2m

So we need to find the highest m for which 2^2m divides 30!.

30/2 = 15 (take only the quotient)
15/2 = 7 (take only the quotient)
7/2 = 3 (take only the quotient)
3/2 = 1 (take only the quotient)

When you get a quotient that is not divisible by the divisor or will give a fraction, stop. Add all the quotients, and you have the highest power of the number 2 that divides 30!. As you can see, this is 15 + 7 + 3 + 1 = 26.

Therefore 2m=26 or m=13.

Hope this helps.

Now if the question said 4m divides 30!, you just need to find the highest number that divides 30!/4, which is again 13.



sorry in advance if this is a dumb question, but I understand your explanation, but does this alway work? Do I always have to bring it to a base of 2 and then do what you did? What happens if it was not 4^m, but 5^m? Thanks
  [#permalink] 28 Jun 2006, 16:06
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic M20-02. If x is a prime number, what is the greatest factor Bunuel 1 23 May 2014, 08:51
2 Experts publish their posts in the topic If m = 3^n, what is the greatest value of n for which m is a hb 2 23 Jul 2013, 06:52
Experts publish their posts in the topic (x + 7) is a factor in x^2 - mx - 56. What is the value of m Archit143 2 05 Dec 2012, 07:00
43 Experts publish their posts in the topic What is the greatest value of m such that 4^m is a factor of rxs0005 18 03 Dec 2010, 17:12
What is the greatest value of x such that 8^x is a factor of tarek99 6 17 Oct 2008, 06:27
Display posts from previous: Sort by

What is the greatest value of m such that 4m is a factor of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.