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Microsoft Excel 2007 Formula Question

I have an Excel worksheet (named "Consolidated") where Column A is "Date", Column B is called "Type of Review." Each of these columns have different names and dates associated with them. In column F I have a value. So for example:
Column A        Column B         Column F
4/9/2012            Type A            100
4/9/2012            Type B             50
4/10/2012          Type A            110
4/10/2012          Type B             50

Rather than run a Pivot Table, which I am aware of, I have a new worksheet (named "Aggregate") where I am looking to sum/aggregate all of Column F by what it is labeled in Column B -- so here I would have Type A = 210 (regardless of the date) and Type B = 100. One of my colleagues recommended a sumproduct for getting this result. I am a beginner so detailed help would be useful and appreciated.
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Quick response, exactly what I needed. If you could do an overview of sumproduct function that would be very helpful as well.
You may find Microsoft Excel MVP Bob Phillip's web page on SUMPRODUCT to provide a good explanation of how it works: http://www.xldynamic.com/source/xld.SUMPRODUCT.html