Posted by **Sam** on Tuesday, November 28, 2006 at 10:17am.

Amy has a collection of X,Y, and Z's. Every X is a Y. One-half the Z's are Y's. There are 3 times as many Y's as X's. Amy has 50 Z's and 40X's.

No Z in an X.

How many Y's does Amy have that are neither X's nor Z's?

I found drawing a venn diagram helps solve this problem. There are 120 Ys, 40 XYs, and 25YZs. So, Ys only = 120-40-25 = 55