A mystery number is even and has 2 digits. The difference between the digits is 3. The digit in the ones place is between 0 and 4. What is the...

Hello!

Denote our number as `XY,` it has `Y` ones and `X` tens.

A number is even if and only if its digit at the ones' place is even. Really, a two-digit number `XY` is equal to `Y+10*X.`  

If `Y` is even (divisible by 2), then `Y=2*Z` and `Y+10*X = 2*Z+10*X = 2*(Z+5*X)` which is even.

And if `Y+10*X` is even, `Y+10*X=2*W,` then `Y = 2*W-10*X = 2*(W-5*X)` is also even.

So `Y` is even and is between 0 and 4. If "between" means that 0 and 4 are NOT allowed, then `Y=2` (the only even number which is >0 and <4).

The difference between the digits is 3 means `X-Y=3` or `Y-X=3.`

But if `Y=2` then the second variant, `Y-X=3,` `Y=2=3+X` is impossible, so `X-Y=3` and `X=Y+3=5.`

The answer: the number is 52.

P.S. For me, "between 0 and 4" means that 0 and 4 ARE allowed. Then Y may be not only 2, but also 0 and 4. This gives several more answers, namely 30, 74 and 14.