Multiple choice

Two newpapers $A$ and $B$ are published in a city. It is known that $25$% of the city population reads $A$ and $20$% reads $B$ while $8$% reads both $A$ and $B$. Further, $30$% of those who read $A$ but not $B$ look into advertisements and $40$% of those who read $B$ but not $A$ also look into advertisements while $50$% of those who read $A$ and $B$ look into advertisements. Then the percentage of the population who look into advertisement is:

  1. $12.8$
  2. $13.5$
  3. $13.9$
  4. $13$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P(A only) = 25 - 8 = 17%. P(B only) = 20 - 8 = 12%. P(Both) = 8%. Ads = (0.3 * 17) + (0.4 * 12) + (0.5 * 8) = 5.1 + 4.8 + 4.0 = 13.9%.

AI explanation

First, determine the percentage of the population that reads only newspaper A by subtracting the overlap from A's readers, giving 25 percent minus 8 percent, which equals 17 percent. Next, find those who read only B by subtracting the overlap from B's readers, yielding 20 percent minus 8 percent, which is 12 percent. Calculate the advertisement viewers from each group: 30 percent of 17 percent is 5.1 percent, 40 percent of 12 percent is 4.8 percent, and 50 percent of the 8 percent overlap is 4 percent. Adding these viewer groups together gives 5.1 percent plus 4.8 percent plus 4.0 percent, totaling 13.9 percent of the population.