We know that a messenger will deliver exactly seven packages: L, M, N, O, P, S, and T.
The packages will be delivered one at a time. Therefore, this is a linear game.
_ _ _ _ _ _ _ 1 2 3 4 5 6 7
Now let's go through our conditions.
Rule 1 - P is delivered either first or seventh
P1 or P7
Rule 2 - the messenger delivers N at some time after delivering L
L > N
Rule 3 - the messenger delivers T at some time after delivering M
M > T
Rule 4 - the messenger delivers exactly one package between delivering L and delivering O, whether or not L is delivered before O
|L_O| or |O_L|
Rule 5 - the messenger delivers exactly one package between delivering M and delivering P, whether or not M is delivered before P
|M_P| or |P_M|
If the order is |M_P|, then P must be delivered seventh. It cannot be delivered first because M and one other package must precede it.
If the order is |P_M|, then P must be delivered first. It cannot be delivered seventh because M and one other package must follow it.
We can combine Rules 2 and 4 and Rules 3 and 5 to give us a couple different options.
Rules 2 and 4
1) LNO 2) L_O > N 3) O_L > N
Rules 3 and 5
1) MTP 2) M_P > T 3) P_M > T
Now let's address the question stem. We are looking for the answer choice which could be true if N is delivered fourth.
_ _ _ N _ _ _ 1 2 3 4 5 6 7
Answer choice (B) cannot be true because of the first three scenarios we have outlined above. If N is fourth, then L could only be first or third.
_ _ L N O _ _ (note that this scenario cannot be true because we need to fit in the |M_P| or |P_M| block) 1 2 3 4 5 6 7
L _ O N _ _ _ 1 2 3 4 5 6 7
O _ L N _ _ _ 1 2 3 4 5 6 7
Answer choice (C) cannot be true because of the scenarios we have outlined addressing answer choice (B). As N is delivered fourth, |L_O| or |O_L| must be delivered first, second, and third as L must precede N.
Answer choice (D) is incorrect for the same reason as answer choice (C). O can only be delivered first or third.
Answer choice (E) is incorrect for the same reason as above. The first package delivered must be L or O.
Therefore, the correct answer should be (A) but let's double check.
If L is delivered first, then Rule 1 means that P must be delivered seventh and Rule 5 means that M must be delivered fifth. This means that T must be delivered sixth and S must be delivered in the remaining slot i.e. second.
L S O N M T P 1 2 3 4 5 6 7
Notice that this meets all of our conditions and, therefore, could be true:
1) P is delivered seventh 2) N (4) is delivered after L (1) 3) T (6) is delivered after M (5) 4) Exactly one package (S) is delivered between L and O. 5) Exactly one package (T) is delivered between M and P.
Hope this helps! Please let us know if you have any further questions.
jiangchengwangon May 13, 2021
Hi, I am really confused with the last two rules, the last two rule are saying whether or not L is delivered before O and whether or not M is delivered before P. So I am assuming L is always before O and M is always before P.
jiangchengwangon May 13, 2021
I understand that P is either spot 1 or7, so if M is before then P, it's impossible to spot M.
Emil-Kunkinon November 30, 2023
The last two rules are saying that there is always one spot between them, no matter which of the two comes first.
