Question

Let M be the set of all even numbers from 1 to 25 and all the odd numbers between 26 and 200. If all the elements of M are multiplied, find the number of zeroes at the end of this product.

1. 22
2. 18
3. 23
4. 21

Answer 1

We get a 0, when we multiply 2 and 5 together.

For even numbers from 1 to 25, we get 12 + 6 + 3 = 21 2's. For odd numbers from 26-200 we get 25 + 5 + 1 = 31 5's. So, their multiple will have min(21, 31) = 21 zeroes at end.

Comments

Sir, we can get zero by two cases.

I. When we multiply 2 by 5 and

II. When already there is zero at the end.(like in 10)

So taking forward your solution, we get 21 zero's from I case and two more zero's from II case i.e. from 10 and 20.

Final answer would be =21+2=23.

Answer 2

4.21