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SUMPRODUCT Function Between Two Dates

I am using the following function to return a value from Column B if Column A meets certain criteria:

=SUMPRODUCT(--('Brian Chadwick.xlsx'!$A2:$A200>20130505),'Brian Chadwick.xlsx'!$B2:$B200)

This function is working correctly.  However, I need to alter the function to test for a range of  numbers.  IE: >20130505 AND <20130513.  I've tried several variations of the formula with no success. Can anyone help me?
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NBVC
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Or as a multiplication

=SUMPRODUCT(('Brian Chadwick.xlsx'!$A2:$A200>20130505)*('Brian Chadwick.xlsx'!$A2:$A200<20130513)*('Brian Chadwick.xlsx'!$B2:$B200))

Since you have excel 2010, you can also use SUMIFS

=SUMIFS('Brian Chadwick.xlsx'!$B2:$B200,'Brian Chadwick.xlsx'!$A2:$A200,">20130505",'Brian Chadwick.xlsx'!$A2:$A200,"<20130513")


Thomas
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Worked perfectly!  Thank you!