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?

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

Tardigrade Admin · Accepted Answer

See the following Venn diagram n (I) = 29 + 23 = 52 n (F) = 100 - 52 = 48 n(M ∪ D) = n(M) + n(D) - n(M∩ D) 24 = 23+ 4 - n(M∩ D) ∴ n(M∩ D) = 3 ∴ W ∩ D) = 4 -3 = 1

Q. 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?

48, 1

34, 3

46, 4

42, 2

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

Q. 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?

48, 1

34, 3

46, 4

42, 2

See the following Venn diagram n(I)=29+23=52 n(F)=100−52=48 n(M∪D)=n(M)+n(D)−n(M∩D) 24=23+4−n(M∩D) ∴n(M∩D)=3 ∴W∩D)=4−3=1

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