Peanut Butter Sandwiches

Just the facts ma'am:

900 total Peanut Butter sandwiches of varying ilks

600 Peanut Butter and Jelly - PBJ

390 Peanut Butter and Banana - PBB

400 Peanut Butter and Pickle - PBP

250 Peanut Butter, Jelly, and Banana - PBJB

150 Peanut Butter, Jelly, and Pickle - PBJP

200 Peanut Butter, Banana, and Pickle - PBBP

20 Peanut Butter, Jelly, Banana, and Pickle - PBJBP

Remember that any grouping is included inside a larger group.  Such as the 250 Peanut Butter, Jelly, and Banana, is by definition Peanut Butter and Jelly so included in that group of 600.  Think in terms of a Venn diagram.

Now the question is:  How many PB sandwiches are neither Jelly, Banana, or Pickle?

And we're off:

Start with the center of our three circle Venn diagram - 20 PBJBP, which means there are 180 PBBP, 130 PBJP, and 230 PBJB because each of these Venn intersections contain the 20 PBJBP.

Moving outward into the larger circle sections of our Venn Diagram we get 170 PBJ, 70 PBP, and 10 PBB.  Now to compute the remaining Peanut Butter sandwiches we subtract all these sections from our initial 900 sandwiches.

900- 20 - 180 - 130 - 230 - 10 - 70 - 170 = 90 remaining PB sandwiches.