2IIM - CAT Discussion Forum

Counting is one of the under-explored territories as far as CAT are concerned. Here is an example question in this segment

How many zeroes are there at the end of 50!
a. 12
b. 10
c. 8
d. 11

Answer 10 0s.

Every multiple of 5 and a multiple of 2 will give a 0 at the end of the number.

There are 10 multiples of 5, -- 5, 10, ..... 50. And definitely more than 10 multiples of 2.

So, there will be 10 0s.

Is that the correct answer.

Hi Raghav,

That is indeed te starting point. There will definitely be more counts of 2 than 5, so counting 5's is probably the best way to go about this. There are 10 numbers that are multiples of 5 less than 50 as well. However, there are a few numbers that are a multiple of 5^2 as well. These numbers will contribute two zeroes, as it where.

So, the right answer would be 10+2=12. There would be 12 zeroes in 50!.

The logical extension of this question would be - what is the formula to find the number of zeroes in n!?

Cheers