Question 1066746: In a sample of 150 people, 45 swim, 40 bike, and 50 jog. Moreover, 32 jog but don't bike, 27 jog and swim, and 10 do all three activities.
a. How many jog but don't swim and don't bike?
b. If 21 bike and swim, how many do not do any of the activities?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! You need a Venn diagram which is 3 interlocking
circles: swimmers, joggers, and bikers
Realize there are 7 regions, and each has a different
meaning. The center one is all 3: swimmers, joggers, and bikers.
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10 do all 3 activities
27 jog and swim. That leaves 
that jog and swim, but don't do anything else
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(a)
32 jog but don't bike, so if you subtract the joggers and
swimmers, there are  who ONLY jog
but don't swim and bike
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(b)
21 bike and swim. Subtract those who do all 3.
 so, 11 do ONLY swimming and biking.
Now I can subtract  from total swimmers
 who ONLY swim
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Likewise, subtract  from all the joggers
 who ONLY jog or bike
There is only 1 of the 7 regions left. It is those who bike ONLY.
Subtract  from total of bikers
 who ONLY bike
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Now add up all of the 7 regions and subtract from 
There are 71 who don't swim, bike or jog
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Note there is no way to do this problem if you don't draw
a Venn diagram and understand what each of the 7 regions
means. Always start with the center one which is those who
do all 3 activities. Hope this helps.
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