SOLUTION: A plant supervisor reported that of the 20 people being supervised, 16 could operate a lathe, 12 could operate a grinder, 8 could operate a lathe and a bender, 5 could operate all

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Question 493480: A plant supervisor reported that of the 20 people being supervised, 16 could operate a lathe, 12 could operate a grinder, 8 could operate a lathe and a bender, 5 could operate all 3 machines. Should the supervisor be believed? Why or why not?
PLEASE help. I am desperate.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
this is MUCH easier with a Venn Diagram

"5 could operate all 3 machines" ___ 1st group

"8 could operate a lathe and a bender" ___ but 5 of them are from the 1st group, so 3 can operate ONLY lathe and bender
___ 2nd group

"12 could operate a grinder" ___ but 5 of them are from the 1st group, so 7 can operate ONLY a grinder ___ 3rd group

"16 could operate a lathe" ___ but 5 of them are from the 1st group and 3 of them are from the 2nd group
___ so 8 can operate ONLY a lathe ___ 4th group

5 + 3 + 7 + 8 = 23 ___ something is amiss...

no bender or lathe & grinder or bender & grinder?