A builder will build five houses in New Housing Scheme on a street that currently has no houses. The builder will select from seven different models of houses: L,M,N,O,P,Q and R. The Development Authority has placed the following restrictions on the builder: No model can be selected for more than one house. Either model O must be selected or model R must be selected, but both cannot be selected. If model Q is selected, then model N cannot be selected. If model M is selected, then model O cannot be selected. Which of the following is an acceptable combination of models that can be selected for the street? (A) L, M, N, P, Q (B) L, M, P, Q, R (C) L, N, P,Q, R (D) M, N, O, P, Q (E) N, O, P, Q, R
Question
A builder will build five houses in New Housing Scheme on a street that currently has no houses. The builder will select from seven different models of houses: L,M,N,O,P,Q and R. The Development Authority has placed the following restrictions on the builder:
No model can be selected for more than one house. Either model O must be selected or model R must be selected, but both cannot be selected. If model Q is selected, then model N cannot be selected. If model M is selected, then model O cannot be selected. Which of the following is an acceptable combination of models that can be selected for the street? (A) L, M, N, P, Q (B) L, M, P, Q, R (C) L, N, P,Q, R (D) M, N, O, P, Q (E) N, O, P, Q, R
Solution
The acceptable combination of models that can be selected for the street is (B) L, M, P, Q, R.
Here's why:
(A) L, M, N, P, Q - This is not acceptable because if model Q is selected, then model N cannot be selected.
(B) L, M, P, Q, R - This is acceptable. All the restrictions are met. No model is repeated, model R is selected (meeting the requirement that either O or R must be selected), and neither of the restrictions involving models Q, N, M, and O are violated.
(C) L, N, P,Q, R - This is not acceptable because if model Q is selected, then model N cannot be selected.
(D) M, N, O, P, Q - This is not acceptable because if model M is selected, then model O cannot be selected.
(E) N, O, P, Q, R - This is not acceptable because if model Q is selected, then model N cannot be selected.
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