Radio button within a repeater problem

Recently I was developing a system to create tests and test questions.  For these tests our client wanted multiple choice questions.  To implement this I decided to have a list of textboxes for the answer text, and a radio button for each textbox to select the correct answer.   I knew that a RadioButtonList couldn’t have anything other than a radio button and text, so I went with a repeater.

<asp:Repeater ID="rptRadios" runat="server">
    <HeaderTemplate>
        <ul>
    </HeaderTemplate>
    <ItemTemplate>
        <li>
            <asp:RadioButton ID="rbRadio" runat="server" GroupName="RadioGroup" />
            &nbsp;
            <asp:TextBox runat="server" ID="txtRadio"></asp:TextBox>
        </li>
    </ItemTemplate>
    <FooterTemplate>
        </ul>
    </FooterTemplate>
</asp:Repeater>

Doing it this way caused the group name of each radio button to be inconsistent, because of the repeater.  After a while of researching and not finding any good solutions I decided to try changing the group name of the radio buttons using jQuery. 
$("input:radio").attr('name', 'RadioGroup');

That gave me the radio button functionality that I wanted, but it prevented me from getting the selected radio button on postback.  So I decided to just implement the radio button functionality manually.
var radios = $("input:radio");
radios.click(function() {
     radios.removeAttr('checked');
     $(this).attr('checked', 'checked');
     return true;
});

Which gave me the correct functionality and I could still get the selected radio button and textbox on postback.   Probably not the most elegant solution, but I couldn’t find any other way to do it.  
Also I needed to make sure at least one of the radio buttons was selected so I added a CustomValidator that called a javascript function.
function ValidateRadioButtons(sender, args) {
     args.IsValid = $("input:radio:checked").size() > 0;
}