jquery - select an option based on data

Try this instead:

$('#Adjunct_Title_Number').val(response.Adjunct_Title_Number); 

You don't set a select box by setting selected on the options, but by setting the value of the select box with val():

$('#Adjunct_Title_Number').val(response.Adjunct_Title_Number); 

$('#Adjunct_Title_Number option').filter(function() { return this.value == response.Adjunct_Title_Number; }).prop('selected','true'); 

Try surrounding the value with quotes:

$('#Adjunct_Title_Number > option[value="' + response.Adjunct_Title_Number + '"]').attr('selected','selected'); 

First of all check if $('#Adjunct_Title_Number > option[value=' + response.Adjunct_Title_Number + ']') is a defined item (not empty object).

Next you should on older jQuery to remove attribute selected from other items:

$('#Adjunct_Title_Number option').removeAttr('selected').filter(function(){ return ($(this).value == response.Adjunct_Title_Number) }) .attr('selected','selected');