Question 1177066: An advertising agency finds that of its 170 clients, 115 use TV and 110 use radio, 130 use magazine. Also 85 use TV and magazine, 75 use TV and radio, 95 use radio and magazines, 70 use all three. Find:
i) how many use only radio
ii) how many use only TV
iii) how many use TV and magazines and but not radio
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Draw the 3 circles intersecting.
place outside each one the total number
115 TV
110 R
130 M
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70 use all 3
TV+ magazine use 85, but 70 of that is where TV/Mag/Radio are involved, so 15 is in the TV/Mag intersection
Similarly, TV+Radio have 75, but 70 is with them + magazine, so 5 are left for the two jointly.
And Radio + Mag are 95 with 70 all 3, so the joint pair has 25.
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TV has 5 with radio, 15 with magazine and 70 with both, so that leaves 25 for TV only, since it is 115 total.
Radio has 5 with TV, 25 with magazine and 70 with all three, so that leaves 10 for radio.
Magazine has 15 with TV and 25 with radio, 70 with all three, so that leaves 20 for magazine.
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Answers are
i) 10
ii)25
iii)TV is 25, TV and Magazines is 15, and Magazines alone are 20, so that answer is 60.
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