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

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

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New post 11 Aug 2018, 22:29
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Question Stats:

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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

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

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New post Updated on: 11 Aug 2018, 22:43
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.
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Originally posted by Afc0892 on 11 Aug 2018, 22:42.
Last edited by Afc0892 on 11 Aug 2018, 22:43, edited 1 time in total.
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N is the product of all positive multiples of 5 from 1 to  [#permalink]

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New post Updated on: 11 Aug 2018, 23:33
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

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Originally posted by push12345 on 11 Aug 2018, 22:43.
Last edited by push12345 on 11 Aug 2018, 23:33, edited 1 time in total.
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N is the product of all positive multiples of 5 from 1 to  [#permalink]

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New post 11 Aug 2018, 23:12
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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)
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Re: N is the product of all positive multiples of 5 from 1 to  [#permalink]

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New post 13 Aug 2018, 08:24
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?
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Re: N is the product of all positive multiples of 5 from 1 to  [#permalink]

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New post 13 Aug 2018, 20:23
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
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N is the product of all positive multiples of 5 from 1 to  [#permalink]

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New post 13 Aug 2018, 20:36
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.
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PKN

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Re: N is the product of all positive multiples of 5 from 1 to  [#permalink]

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New post 13 Aug 2018, 21:55
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?


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Re: N is the product of all positive multiples of 5 from 1 to &nbs [#permalink] 13 Aug 2018, 21:55
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