On Saturday eight flights j k l m n o p and r are scheduled to depart from a small airport in Darby Field. For safety reasons, no two flights depart at the same time and each flight depart exactly once The flights depart according to the following conditions: Flight R departs some time after L Flight K departs some time after flight P but before R Flight L departs some time before flights O and J Flight M departs some time before flight k and flight N departs some time after flight R Flight J is the seventh flight to depart.
- Each of the following could be forth flight EXCEPT:
a.K
b.R
c.O
d.P
e.M
- If L is the fourth flight to depart, each of the following could be false EXCEPT:
a. M is the second flight to depart
b. O is the eighth flight to depart
c. N is the sixth flight to depart
d. K is the third flight to depart
e. P is the second flight to depart
- If flight N departs before flight O, which of the following could be true?
a. Flight R departs sixth
b. Flight K departs third
c. Flight O departs earlier than flight J
d. Flight K departs fifth
e. Flight M departs fourth
- Which of the following must be true?
a. Flight M departs before flight L
b. Flight P departs before O
c. Flight L departs before N
d. Flight K departs before O
e. Flight L departs before K
- Which of the following could be the order, for the first to last, in which the flights depart?
a. L, P, M, K, R, N , J, O
b. P, K, R, N, L, O, J, M
c. M, L, P, K, R, O, N, J
d. M, K, P, L, O, R, J, N
e. P, M, K, R, L, N, J, O
For 3) note that $N$ can only leave at 6 or 8 and $R$ can only leave at 5 or 6. If $N$ departs before $O$ it departs at 6 and $O$ at $8$, then $R$ has to leave at 5. As $M<K<R$ we find that $K<5$ and $M<4$. $K$ could depart at 3 though, so 3) b.
For 5) we can see that only $N$ and $O$ can depart at 8, so b and c are wrong. Also as mentioned $R>4$ so e is wrong. Also $P<K$ so d is wrong. Leaving a as the only plausible option which indeed does satisfy all conditions. Namely: $$L<R,\ P<K<R<N,\ L<O,\ L<J\text{ and }M<K.$$