Aptitude 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** $(= 5×5×5)$.

**Anand Gupta**

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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.