C++ ignoring else if [duplicate]

The point of this program is to get a 2 digit number input and if the number is smaller or equal to 15, return the number squared, if the number is bigger or equal than 16 and smaller or equal to 30, return the sum of it s digits and if it is bigger or equal to 31, it should return the product of its digits.

This is the code I wrote so far:

#include <iostream>
using namespace std;

int main()
{
    int a;
    cout << "dati a: ";
    cin >> a;
    if (a >= 100 || a)
    {
        cout << "a trebuie sa aiba 2 cifre" << endl
             << "mai dati incercati o data: ";
    }

    if (a <= 15)
    {
        cout << a * a;
    }
    else if (16 <= a <= 30)
    {
        cout << a / 10 + a % 10;
    }
    else if (a >= 31)
    {
        cout << (a / 10) * (a % 10);
    }
}

I compile it and run it and testing goes like this. I give it 10, it returns 100, I give it 23 it returns 5, I give it 29 it returns 11 and the i give it 31 it returns 4, i give it 38, it returns 11. I tend to believe that it goes over the last else if, but i don't know the true reason.