Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 19 Jul 2019, 04:03

### 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

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

# N is the product of all positive multiples of 5 from 1 to

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 22 Aug 2013
Posts: 1435
Location: India
N is the product of all positive multiples of 5 from 1 to  [#permalink]

### Show Tags

11 Aug 2018, 23:29
4
00:00

Difficulty:

65% (hard)

Question Stats:

59% (02:16) correct 41% (02:15) wrong based on 64 sessions

### HideShow timer Statistics

N is the product of all positive multiples of 5 from 1 to 100 inclusive. And x is a positive integer such that N is divisible by 10^x.

What is the highest possible value of x?

A. 16
B. 18
C. 20
D. 24
E. 26

Posted from my mobile device
NUS School Moderator
Joined: 18 Jul 2018
Posts: 983
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
N is the product of all positive multiples of 5 from 1 to  [#permalink]

### Show Tags

Updated on: 11 Aug 2018, 23:43
Given N is a product of all multiples of 5 from 1 to 100.
N = 5x10x15x20x....x100
Writing N in terms of 2s and 5s we have N = $$2^{20}$$*$$5^{24}$$
10 can be written as 2*5. So the maximum number of 10^x can be 20.
Hence C is the ans.
_________________
Press +1 Kudos If my post helps!

Originally posted by Chethan92 on 11 Aug 2018, 23:42.
Last edited by Chethan92 on 11 Aug 2018, 23:43, edited 1 time in total.
Director
Joined: 02 Oct 2017
Posts: 727
N is the product of all positive multiples of 5 from 1 to  [#permalink]

### Show Tags

Updated on: 12 Aug 2018, 00:33
And has to be 18

5 has power of 24
20 multiples of 5
Plus 4 for 25,50 and 75

But 2 is limiting factor here
It has factor of 18

Posted from my mobile device
_________________
Give kudos if you like the post

Originally posted by push12345 on 11 Aug 2018, 23:43.
Last edited by push12345 on 12 Aug 2018, 00:33, edited 1 time in total.
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
N is the product of all positive multiples of 5 from 1 to  [#permalink]

### Show Tags

12 Aug 2018, 00:12
1
1
amanvermagmat wrote:
N is the product of all positive multiples of 5 from 1 to 100 inclusive. And x is a positive integer such that N is divisible by 10^x.

What is the highest possible value of x?

A. 16
B. 18
C. 20
D. 24
E. 26

Posted from my mobile device

Given N=5*10*15*.....*90*95*100
Or, N=$$5^{20}*(1*2*3*....*19*20$$=$$5^{20}*20!$$
We have to find out power of 2 and power of 5 in 20!
$$\frac{20}{5}$$=4
$$\frac{20}{2}+\frac{20}{2^2}+\frac{20}{2^3}+\frac{20}{2^4}$$=10+5+2+1=18
So, N=$$5^{20}*5^4*2^18$$=$$(5*2)^{18}*5^6$$=$$10^{18}*5^6$$

So the maximum value of x for which N is divisible by $$10^x$$ is 18.
Ans. (B)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Manager
Joined: 20 Jul 2018
Posts: 87
GPA: 2.87
Re: N is the product of all positive multiples of 5 from 1 to  [#permalink]

### Show Tags

13 Aug 2018, 09:24
Afc0892 wrote:
Given N is a product of all multiples of 5 from 1 to 100.
N = 5x10x15x20x....x100
Writing N in terms of 2s and 5s we have N = $$2^{20}$$*$$5^{24}$$
10 can be written as 2*5. So the maximum number of 10^x can be 20.
Hence C is the ans.

how did you calculate 2s and 5s in N?
_________________
Hasnain Afzal

"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas
Intern
Joined: 28 May 2017
Posts: 3
Re: N is the product of all positive multiples of 5 from 1 to  [#permalink]

### Show Tags

13 Aug 2018, 21:23
PKN wrote:
amanvermagmat wrote:
N is the product of all positive multiples of 5 from 1 to 100 inclusive. And x is a positive integer such that N is divisible by 10^x.

What is the highest possible value of x?

A. 16
B. 18
C. 20
D. 24
E. 26

Posted from my mobile device

Given N=5*10*15*.....*90*95*100
Or, N=$$5^{20}*(1*2*3*....*19*20$$=$$5^{20}*20!$$

Hi,

Given N=5*10*15*.....*90*95*100
This should be 5 (1*2*3*4.....*19*20) i.e. 5 * 20!
How did you arrive at 5^20 * 20! Kindly explain

Thanks,
Chirag
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
N is the product of all positive multiples of 5 from 1 to  [#permalink]

### Show Tags

13 Aug 2018, 21:36
1
chiragmaniar wrote:
PKN wrote:
amanvermagmat wrote:
N is the product of all positive multiples of 5 from 1 to 100 inclusive. And x is a positive integer such that N is divisible by 10^x.

What is the highest possible value of x?

A. 16
B. 18
C. 20
D. 24
E. 26

Posted from my mobile device

Given N=5*10*15*.....*90*95*100
Or, N=$$5^{20}*(1*2*3*....*19*20)$$=$$5^{20}*20!$$
Hi,
Given N=5*10*15*.....*90*95*100
This should be 5 (1*2*3*4.....*19*20) i.e. 5 * 20!
How did you arrive at 5^20 * 20! Kindly explain

Thanks,
Chirag

Hi chiragmaniar,
5=5*1
10=5*2
15=5*3
.
.
.
100=5*20
x(multiply)
------------------
N=(5*1)*(5*2)*(5*3)*......................*(5*20)
Or, N={5*5*5*....(20 times)}* (1*2*3*.....*20)
Or, $$N=(5^{20})* (20!)$$

Hope it clarifies.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9446
Location: Pune, India
Re: N is the product of all positive multiples of 5 from 1 to  [#permalink]

### Show Tags

13 Aug 2018, 22:55
1
hasnain3047 wrote:
Afc0892 wrote:
Given N is a product of all multiples of 5 from 1 to 100.
N = 5x10x15x20x....x100
Writing N in terms of 2s and 5s we have N = $$2^{20}$$*$$5^{24}$$
10 can be written as 2*5. So the maximum number of 10^x can be 20.
Hence C is the ans.

how did you calculate 2s and 5s in N?

Check this post for a detailed discussion: https://www.veritasprep.com/blog/2011/0 ... actorials/
_________________
Karishma
Veritas Prep GMAT Instructor

Re: N is the product of all positive multiples of 5 from 1 to   [#permalink] 13 Aug 2018, 22:55
Display posts from previous: Sort by