Ruby:

(1..100).each do |i|                     # Built-in support for ranges, iterator blocks
  str = ''
  str << 'Fizz' if i % 3 == 0            # Mutable strings, postfix conditionals
  str << 'Buzz' if i % 5 == 0
  puts str.empty? ? i : str  
end

Great question! FizzBuzz is indeed one of the most well known screening questions asked in interviews. I remember coming across a cool Python solution that got it done using generators, without resorting to any modulo logic. Here's how you'd do it in JavaScript, using generators. :-)

(function () {
    function* yieldFizzAt3() {
        while (true) {
            yield '';
            yield '';
            yield 'Fizz';
        }
    };

    function* yieldBuzzAt5() {
        while (true) {
            yield '';
            yield '';
            yield '';
            yield '';
            yield 'Buzz';
        }
    };

    var fizz = yieldFizzAt3();
    var buzz = yieldBuzzAt5();

    for (var i = 1; i < 101; i++) {
        var fizzBuzz = fizz.next().value + buzz.next().value;
        console.log(fizzBuzz ? fizzBuzz : i);
    }
})();

for(int i = 0; i <= 100; i++){
Console.WriteLine(i % 3 == 0 && i % 5 == 0 ? "FizzBuzz" : i % 3 == 0 ? "Fizz" : i % 5 == 0 ? "Buzz" : i.ToString());

}

That's how I resolved it during an interview, using C#

well i would go for a nested if

if number modulo 3 and number modulo 5 
    write FizzBuzz
else if number modulo 3 
     write Fizz
else if number modulo 5
    write Buzz
else 
    write number

so if we wanna reduce the amount of operations by two we could assign

mod3 = number modulo 3
mod5 = number modulo 5

if mod3 and mod5 
.....

or did i missunderstand the problem ? or do you want examples of different languages ? ;D ....