Bunuel
In a locality of 40 houses, each house is subscribed to at least one newspaper from amongst, The Sun, Daily Mail and Daily Mirror. 24 houses subscribe to Daily Mirror. 13 houses subscribe to both The Sun and Daily Mirror. 26 houses subscribe to Daily Mail out of which 16 also subscribe to The Sun. There is no house which subscribes to The Sun alone. 7 houses subscribe to all three newspapers. How many houses subscribe to only two newspapers?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Option-DSol: Solution using the overlapping sets formula (if nothing else works out for you)
Designate Sun as "S", Daily Mail as "D" and Daily Mirror as "M"
Total House = 40 ---> P(S u D u M) = 40
Each House has at least 1 ---> P(Neither)=0
24 houses subscribe to Daily Mirror ----> P(M)=24
13 houses subscribe to both The Sun and Daily Mirror ----> P(M n S) = 13
26 houses subscribe to Daily Mail out of which 16 also subscribe to The Sun -----> P(D) = 26 and P(S n D) = 16
7 houses subscribe to all three newspapers - P (S n D n M) = 7
There is no house which subscribes to The Sun alone: If no house subscribes to The Sun alone, P(S) = P(S n D) + P (M n S) - P (S n D n M) = 13+16-7 = 22
(The intersection of the three is subtracted because it is counted twice)
Now,
P(S u D u M) = P(S) + P(D) + P(M) - P(S n D) - P(D n M) - P(M n S) + P (S n D n M)
From above, P(D n M) can be calculated as 10.
Only 2 are given as : P(S n D) + P(D n M) + P(M n S) - 3*P (S n D n M) = 10 + 13 + 16 - 3*7 = 18