Solve the problem.
-Among a group of 85 investors, 27 owned shares of Stock A, 34 owned shares of Stock B, 44 owned sharesof Stock C, 12 owned shares of both Stock A and Stock B, 13 owned shares of Stock A and Stock C, 18owned shares of Stock B and Stock C, and 8 owned shares of all three. How many investors did not haveshares in any of the three? How many owned shares of either Stock A or Stock C but not Stock B?
A)15; 36
B)23; 31
C)15; 31
D)15; 39

Question

Quizplus · Accepted Answer

15; 36To find the number of investors who did not have shares in any of the three stocks, we use the principle of inclusion-exclusion. The total number of investors owning shares in at least one stock is given by the sum of investors in each stock minus the sum of investors in each pair of stocks plus the number of investors in all three stocks: $27 + 34 + 44 - (12 + 13 + 18) + 8 = 70$. Therefore, the number of investors without shares in any of the three stocks is $85 - 70 = 15$.For the second part, we need to find the number of investors who owned shares of either Stock A or Stock C but not Stock B. This can be calculated by adding the number of investors in Stock A only, Stock C only, and those in both A and C but not in B. The number of investors in A only is $27 - 12 - 13 + 8 = 10$, in C only is $44 - 18 - 13 + 8 = 21$, and those in both A and C but not B is $13 - 8 = 5$. Adding these gives $10 + 21 + 5 = 36$.

Solve the Problem. -Among a Group of 85 Investors, 27 Owned Shares of Owned