Question

At a certain conference of 100 people, there are 29 Indian women and 23 Indian men. Of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. How many foreigners and women doctors are attending the conference?

• A. 48, 1
• B. 34, 3
• C. 46, 4
• D. 42, 2

Answer 1

Answer: (A)

48, 1

Answer 2

See the following Venn diagram $n (I) = 29 + 23 = 52$ $n (F) = 100 - 52 = 48$ $n(M \cup D) = n(M) + n(D) - n(M\cap D)$ $24 = 23+ 4 - n(M\cap D)$ $\therefore n(M\cap D) = 3$ $\therefore W \cap D) = 4 -3 = 1$