Question

I am a number less than 100. When you divide me by 2, my remainder is 1. When you divide me by 25, my remainder is 2. What numbers am I?

Answer 1

27 and 77

Explanation:

Given

Let

`n \to` number

`n\ \%\ 2 = 1`

`n\ \%\ 25 = 2`

`n <100`

Required

Find n

`n\ \%\ 2 = 1` implies that the number is odd and the possible solutions are:

`\{3,5,7,9,......99\}`

The possible solutions to
`n\ \%\ 25 = 2` are:

`\{27,52,77\}`

Testing 27, 52 and 77 with
`n\ \%\ 2 = 1`, we have:

`27\ \%\ 2 = 1` --- true

`52\ \%\ 2 = 0` ---- false

`77\ \%\ 2 = 1` --- true

Hence, the possible numbers are 27 and 77