I googled your question about cutting FQs. I also remembered I'd printed off a FQ cutting diagram & found that in my notebook. Go to nickelquilts | Quilting Blog by Pat Speth. Since I don't know how to do the link, enter May 17, 2012 in the search box. On another web site, UCreate, they list how many squares you can get out of a FQ:

6 - 6.5" squares
9 - 6"
12 - 5.5" or 5"
16 - 4.5"
20 - 4"
30 - 3.5"
42 - 3"
56 - 2.5"
99 -2"

I've made several Turning Twenty quilts; these use 20 FQs, which makes ~ a twin size quilt.

Good luck with your project.