If x=1^1∗2^2∗3^3∗4^4∗...∗98^98∗99^99∗100^100 : Crackverbal Support

If x=1^1∗2^2∗3^3∗4^4∗...∗98^98∗99^99∗100^100 Print

Modified on: Tue, 12 Oct, 2021 at 12:40 PM

Concept: The question tests on the application in Number Properties

Solution:

A zero is the result of the product of a 5 and a 0.

In the question above, all the 5's come from the multiples of 5, like 5, 10, 15, 20 and so on . The 2's come from even numbers. We need to count only the fives as there are more 2's than 5's.

5^5 contributes 5 zeroes

10^10 contributes 10 zeroes

15^15 contributes 15 zeroes

20^20 contributes 20 zeroes

25^25=(52)^25=5^50 contributes 50 zeroes

So all the numbers where we have squares of 5 will give us the double number of zeroes. These numbers are 25, 50, 75 and 100...All other multiples will give us the same number of zeroes as the number itself.

So we have 5 + 10 + 15 + 20 + 50 + 30 + 35 + 40 + 45 + 100 + 55 + 60 + 65 + 70 + 150 + 80 + 85 + 90 + 95 + 200 = 1300

Option A

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If x=1^1∗2^2∗3^3∗4^4∗...∗98^98∗99^99∗100^100 Print

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