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

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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

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