my callback function always evaluate to true

I would like to sum the args of my function if and only if the two args are numbers (hence my first function).

function checkNum() {
 var num = 0;
 for (var i = 0; i < arguments.length; i++) {
  if (typeof arguments[i] !== 'number') {
   return false;
  } 
 }
 return true;
}

function addTogether() {
  var num = 100; 
  if ( checkNum() ) { 
    return arguments[0] + arguments[1];
  } else {
    return undefined;
 }
}
addTogether(2, "");

However my second function performs the sum no matter what the args values are. Any hints on how to fix this ?