Number System
Aptitude

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Q.

How many 3-digit numbers do not have an even digit or a zero?

 A.

60

 B.

80

 C.

125

 D.

150

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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.