The first and last messages on the answering machine could be the first and second messages left by which one of the ...

Irina August 20, 2019

@ishadoshi,

Great job on getting the correct answer!

Since the question requires that one person leaves exactly two messages, we can conclude that G left 0 messages. If G were selected, then everyone would leave one message, which would violate the conditions of this question. It means that we can only use a combination of F P T H L to fill all six slots - 4 of them leaving 1 message, and 1 - 2 messages - to produce a combination that could be true.

(B) is incorrect because if H is #1, P must be #6 per rule 3, so H cannot be #1 and #6.
(C) is incorrect because all H must precede any of L per rule (6), so L cannot be #1 as it is impossible for H to precede it in this scenario.
(D) is incorrect because all P must precede any of T per rule (5), so P cannot be #6 as it is impossible for P to precede T in this scenario.
(E) is incorrect for the same reason - because all P must precede any of T per rule (5) and all T must then follow all P, T cannot be #1 as it is impossible for P to precede T in this scenario.

Please also see below for a more detailed explanation from a previous thread for further reference:


6 messages on the answering machine were left by some combination of FGHLPT. Notice that there is no requirement that each of the persons left at least one message, meaning it is possible that someone left 0 messages.

Now let's look at the rules.

(1) At most one person left more than one message.
(2) No person left more than three messages.

What does this mean for matching names to messages?

It means at most one person left two or three messages.

If one person left two messages, then four left one message, and one left 0 messages.
If one person left three messages, then three left one message, and 2 left 0 messages.

There is no requirement though that anyone leaves more than one message, so a scenario where everyone leaves one message is also equally plausible.

(3) If the first is H, then last is P

H(1) ->P(6)

H P
__ __ __ __ __ __
1 2 3 4 5 6

(4) if G left any message, so did F & P.

G ->F&P

(5) if F left any message, so did P & T, all of P preceding any of T

F->P&T

we can combine this rule with (4) to conclude that
G->F&P&T

P >> T

Since all of P messages must precede any of T if F left any messages, we can also conclude per rule (3) that if H left the first message, G left none because in that scenario P left message #6, and it is impossible for any T messages to follow.

(6) If P left any message, H & L did also, all of H preceding any of L.

P -> H&L
H >> L

we can combine this rule with (4) & (5):

G->F&P &T &H&L

It turns out if G left any messages, then each person left exactly one message and no one left more than one message.

The question asks us who could be the author of the first and last messages on the answering machine?

We can right away eliminate answer choice (B) per rule (3) because if H leaves message #1, P must leave message #6.

We can also eliminate (C), (D), (E) per rules (5) (6). Since all H must precede all L, L cannot be #1. Since all P must precede all T, T cannot be #1, and P cannot be #6 because if P is #6 - all P messages cannot possibly precede all T messages.

Let's try the remaining answer choice (A):

F F
__ __ __ __ __ __
1 2 3 4 5 6

PTHL must also be selected per rules (5) and (6) but the exact order does not matter as long as P > T and H >L thus a complete order could be as follows:

F P H T L F
__ __ __ __ __ __
1 2 3 4 5 6


Since F could be #1 and #6, (A) is the correct answer choice.

Gabe85 June 13, 2020

Hello,

Thanks for this explanation. I immediately understood why A works, and why B and C didn't, but I had to use your explanation for why D and E did not work. I thought that P H L T P P and T P H L T T would work. From your explanation, this seems not to be the case because P>T. However, I thought this only applied to if there was an F. Could you help me with the language of the rule?
The rule says:

If Flueure left any message, Pasquale and Theodore did also, all of Pasquale's preceding any of Theodore's.

basically if F__>P&T, and P>T. However, I thought P>T only applied to if F was present, as this rule is in the same line with an "if" and there is no period or semi colon to separate the ideas, and they seem to be sentence fragments. Could you explain how you understood P>T always applies, and not just with F?

Irina states in the explanation for question 49 that
"@jonah-Mead-Vancort,
It depends - P>T condition applies only if F left any messages."
So it seems another tutor believes this is the case as well? Thus, for this question, P H L T P P and T P H L T T would seemingly work since H>L and since there is no F, P does not have to be > T.

I will attempt to check P H L T P P against the rules:

-At most one person left more than one message.
only P leaves multiple

-No person left more than three messages.
P leaves 3, which is not more than 3.

-If the first message is Hildy's, the last is Pasquale's.
H1-->P6, but can't just reverse so p6-->h1 is invalid, P6 is ok even without H1

-If Greta left any message, Fleure and Pasquale did also.
no G

-If Fleure left any message, Pasquale and Theodore did also, all of Pasquale's preceding any of Theodore's.
No F so P>T does not apply, per my interpretation and Irina's interpretation of the language.

-If Pasquale left any message, Hildy and Liam did also, all of Hildy's preceding any of Liam's.
We have P, so H>L which is not violated.

With the same logic, T P H L T T seems to work as well, IF P>T only applies if F.

Could you help with explaining the wording of this question?

Thank you!

Motunrayo-Bamgbose-Martins July 2, 2020

Exactly! Please I need help because I also thought that applies only if F is present??