If Anna flies in plane 4 and Dave flies in plane 2, which one of the following must be true?

Charlotte on August 9, 2019

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Can you please explain this game? Is there something missing?

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Irina on August 9, 2019

It is a tricky game indeed! Let's look at the setup:

(1) 4 planes 1,2,3,4 are available to fly. Notice the word "available," it means that there is no requirement that all actually do fly.

(2) 3 pilots -ABC, and 3 copilots - DEF are ALL aboard planes.

(3) No plane flies in the show without a qualified pilot.

These two rules tell us that there are at most three planes actually flying in the show because no plane can fly without a pilot.

p ___ ___ ___ ___
c ___ ___ ___ ___
1 2 3 4

(4) A only flies in either #1 & #4
(5) D only flies in either #2 or #3

These rules tell us that there is a minimum of 2 planes flying the show, since someone other than A has to fly the plane that D is on. Combined with the previous rules, we know that we have at least 2 and at most 3 planes participating in the show.

p /A ___ ___ /A
c ___ /D /D ___
1 2 3 4

Let's look at the scenario in question:

If A flies in #4 and D flies in #2, which of the following MUST be true?

p ___ ___ A
c ___ D ___ ___
1 2 3 4

This setup shows us that planes #2 and #4 definitely fly in the show, and at most one other plane - either plane #1 or #3 but not both could fly in the show. Let's look at the answer choices:

(A) C flies in #1 and #3. It could be true that she flies in #1 or #3, but it could also be true that C flies in #2 and B flies in #1 or #3. Since it only could be true, and we are looking for a MUST BE TRUE answer, (A) is wrong;

(B) If C flies in #3, B flies in #2. Let's quickly diagram this:

p ___ C A
c ___ D ___ ___
1 2 3 4

If C is #3 and A is #4, someone has to pilot #2 with copilot D in it, since D cannot fly plane #2 alone. Since we only have 1 pilot left - B, he MUST pilot plane #2, thus this is the correct answer choice. Plane #1 is out of the show since we assigned all 3 pilots.

Let's briefly look at the remaining options:

(C) B and 1 other person fly in plane 1. That again could be true, B could fly plane #1, and C could fly #2. plane #3 is out of the show in this scenario. But B could also fly plane #3 with another person, and plane #1 would be out of the show. Since this answer choice is could be true rather than MUST BE TRUE, it is wrong.

(D) If B is aboard #4, C flies in #3. This is impossible, someone needs to fly #2 and if A & B is aboard #4 and C flies #3, then no pilots are available for plane #2.

(E) If C flies in #2, B flies in #3. It could be true, but it is also possible for C to fly #2 and B fly #1, or B fly #2 and C fly #1 or # 3. Thus, this is only one of many possible options and is not a MUST BE TRUE choice we are looking for.

Does this make sense?

Let me know if you have any further questions.

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