Question 293564
the "VENNGRAM" is three intersecting circles, surrounded by a box


the box represents the 160 dancers surveyed
___ the circles represent the Salsa, Merengue, and Cha Cha


start on the INNERMOST parts of the circles, and work your way out


47 dancers knew all three, so this number goes in the INTERSECTION OF ALL THREE CIRCLES


70 knew the Merengue and Cha Cha, so this number goes in the intersection of the M and CC circles
___BUT ___ there are already 47 in the intersection from the people who knew all three
___ so 23 (70 - 47) are added to the M and CC intersection [question(d)]


similarly for S and CC ___ 4 people added
___ and M and S ___ 30 people added


86 knew the Cha Cha ___ BUT ___ 47 knew all three; 23 knew M and CC; and 4 knew S and CC
___ so 12 (86 - 47 - 23 - 4) are added to the CC circle [part of question(c)]


similarly for Salsa ___ 17 added [question(a)] and [part of question(c)]
___ and Merengue ___ 20 added [question(b)] and [part of question(c)]


(e) 160 dancers MINUS everyone in the three circles
___ 160 - 47 - 23 - 4 - 30 - 12 - 17 - 20 = ?