# Easy Number System Solved QuestionAptitude Discussion

 Q. How many 3-digit numbers do not have an even digit or a zero?
 ✖ A. 60 ✖ B. 80 ✔ C. 125 ✖ D. 150

Solution:
Option(C) is correct

There are 5 digits that are not even or zero: $1, 3, 5, 7$ and $9$.

Now, let’s count all the three-digit numbers that can be formed from these five digits.

The first digit of the number can be filled in 5 ways with any one of the mentioned digits.

Similarly, the second and third digits of the number can be filled in 5 ways.

Hence, the total number of ways of forming the three-digit number is 125 $(= 5×5×5)$.

## (1) Comment(s)

Anand Gupta
()

Alternative interpretation: three digit numbers do not have even or zero : {111, 113, 115, 117, 119} {131, 133,135, 137, 139} . Basically 5 such digits in a group of 20 . Therefore, total digits will be 25 x 8 = 200. Above solution is true if digits are not allowed to be repeated.