|
Author |
Message |
|
TAGS:
|
|
|
VP
Joined: 14 Sep 2005
Posts: 1001
Location: South Korea
Followers: 1
Kudos [?]:
10
[0], given: 0
|
48! + 49!)/10^n is an integer. What is the maximum value of [#permalink]
 14 Dec 2005, 07:18
Question Stats:
0% (00:00) correct
 0% (00:00) wrong based on 0 sessions
(48! + 49!)/10^n is an integer.
What is the maximum value of n?
(Answer choices not available)
_________________
Auge um Auge, Zahn um Zahn  !
|
|
|
|
|
|
|
SVP
Joined: 30 Sep 2004
Posts: 1548
Location: Germany
Followers: 4
Kudos [?]:
15
[0], given: 0
|
(48!+49!)/10^n => 48!(50)/10^n=>largest power of 10^n that divides 48! is 10 and largest power of 50 is 1...hence 11 !
_________________
If your mind can conceive it and your heart can believe it, have faith that you can achieve it.
|
|
|
|
|
|
VP
Joined: 14 Sep 2005
Posts: 1001
Location: South Korea
Followers: 1
Kudos [?]:
10
[0], given: 0
|
christoph wrote: (48!+49!)/10^n => 48!(50)/10^n=>largest power of 10^n that divides 48! is 10 and largest power of 50 is 1...hence 11 !
Isn't the largest power of 50 is 2?
50 is 5 x 10, and there are plenty of 2s in 48!.
So I guess we can make two 10s from 50.
What do you think?
(However, I do not have an OA for this question)
_________________
Auge um Auge, Zahn um Zahn !
|
|
|
|
|
|
Intern
Joined: 15 May 2005
Posts: 12
Location: Somewhere
Followers: 0
Kudos [?]:
0
[0], given: 0
|
uhmm, n max = 12 right?
48!+49!= 48! * 50
5*even = 10
15*even = 10
25*even = 10^2
35*even = 10
45*even = 10
and 10, 20, 30, 40
50*even=10^2
Therefore, n max = 12
|
|
|
|
|
|
SVP
Joined: 30 Sep 2004
Posts: 1548
Location: Germany
Followers: 4
Kudos [?]:
15
[0], given: 0
|
gamjatang wrote: christoph wrote: (48!+49!)/10^n => 48!(50)/10^n=>largest power of 10^n that divides 48! is 10 and largest power of 50 is 1...hence 11 ! Isn't the largest power of 50 is 2? 50 is 5 x 10, and there are plenty of 2s in 48!. So I guess we can make two 10s from 50. What do you think? (However, I do not have an OA for this question) yes ur right...i lost my concentration somewhere... 
_________________
If your mind can conceive it and your heart can believe it, have faith that you can achieve it.
|
|
|
|
|
|
Current Student
Joined: 28 Dec 2004
Posts: 3439
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 11
Kudos [?]:
134
[0], given: 2
|
OK let me take a knock at this.....I am a bit rusty...
(48!+49!)/10^n
well lets first break 10^n into its prime factors 2^a * 5^b....well obviously the power of 5 will be the limiting case here, and so N cannot be greater than b.....
OK now lets re-write 48! +49! into something more easy...48!*50
oK so lets see how many 5s are there in 50,
50/5=10, 50/25=2, so there are 12 5s from 50...
now 48!, has a 5 from 5, 10, 15, 20, 30, 35, 40, 45 plus 2 5s from 25... so 48! gives 10 5s ....so in all as we can see....the power of N=12+10....22!
|
|
|
|
|
|
VP
Joined: 22 Aug 2005
Posts: 1133
Location: CA
Followers: 1
Kudos [?]:
8
[0], given: 0
|
fresinha12 wrote: OK let me take a knock at this.....I am a bit rusty...
(48!+49!)/10^n
well lets first break 10^n into its prime factors 2^a * 5^b....well obviously the power of 5 will be the limiting case here, and so N cannot be greater than b.....
OK now lets re-write 48! +49! into something more easy...48!*50
oK so lets see how many 5s are there in 50,
50/5=10, 50/25=2, so there are 12 5s from 50...
now 48!, has a 5 from 5, 10, 15, 20, 30, 35, 40, 45 plus 2 5s from 25... so 48! gives 10 5s ....so in all as we can see....the power of N=12+10....22!
fresinha12, i guess you thought its 50! not 50.
50 has 2 5's
total: 10 + 2 = 12
_________________
Whether you think you can or think you can't. You're right! - Henry Ford (1863 - 1947)
|
|
|
|
|
|
Current Student
Joined: 28 Dec 2004
Posts: 3439
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 11
Kudos [?]:
134
[0], given: 2
|
you are correct...man...I am so out of it...
50=5*10...so 10=5*2...therefore you get 2 5s...
duttsit wrote: fresinha12 wrote: OK let me take a knock at this.....I am a bit rusty...
(48!+49!)/10^n
well lets first break 10^n into its prime factors 2^a * 5^b....well obviously the power of 5 will be the limiting case here, and so N cannot be greater than b.....
OK now lets re-write 48! +49! into something more easy...48!*50
oK so lets see how many 5s are there in 50,
50/5=10, 50/25=2, so there are 12 5s from 50...
now 48!, has a 5 from 5, 10, 15, 20, 30, 35, 40, 45 plus 2 5s from 25... so 48! gives 10 5s ....so in all as we can see....the power of N=12+10....22! fresinha12, i guess you thought its 50! not 50. 50 has 2 5's total: 10 + 2 = 12 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
close
