(SOLUTION TO INSTALL GOOGLE APPS SYNC FOR OUTLOOK 2010 WITH OFFICE 2013 APPS INSTALLED)
1. regedit.exe
2. Rename
HKEY_LOCAL_MACHINE\Software\Microsoft\Office\15.0
HKEY_LOCAL_MACHINE\Software\Wow6432Node\Microsoft\Office\15.0
to
HKEY_LOCAL_MACHINE\Software\Microsoft\Office\15.0.org
HKEY_LOCAL_MACHINE\Software\Wow6432Node\Microsoft\Office\15.0.org
3. Download and installed Google Apps Sync for Outlook.
4. After installed and config, rename office 15 reg keys back to original name.
My solution worked because I have Outlook 2010. This may not work for you if you have click to run office