Excel: Sum all quantities of unique items across all sheets

I have data spread across several sheets that includes (amongst other things) a part number and a quantity associated with that part. The part number and quantity appears many times in each sheet. I want to SUM all of the quantities for each part number across all sheets.

Example of the data in one of the sheets:

Qty.   Part Number   Description   Price 3       ABC123       Widget 1      $123 2       AAA111       Widget 2      $111 5       ZZZ321       Widget 3      $222 8       ABC123       Widget 1      $123 1       ZZZ321       Widget 3      $222

This format is the same across several sheets. Let's say for example I had 3 sheets of the same data shown above - I want to put the Qty. value for each Part Number into a 4th sheet such that ABC123 = 33, AAA111 = 6, and ZZZ321 = 12.

I was able to do this with a PivotTable, however this is not useful for me because I need to manipulate this data in ways that breaks the PivotTable. Any ideas?