Definintely a head-scratcher! I would rate this question about 750 although note you don't actually need ANY math theory or content to answer it. This question is testing your nerve. If you patiently reason your way through it, it can certainly be done inside of 2 to 2.5 minutes. Of course, trusting that you can get through it quickly enough while "patiently reasoning your way through it" takes nerve or guts.
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Can three of these five pilots ever meet together?
From the stem we know that D is able to meet ANY time B cannot. This means that D is able to meet when B cannot, and also allows for (but does not establish) the possbility that B or D are both able to meet.
Other than that, we don't know that the other pilots are or are not able to meet, and we also don't know whether certain pilots, if able to meet, are or are not able to meet certain other pilots. There's a lot we don't know.
Therefore, in order to be sufficient, the statements will have to provide us with a lot of information. (It would be a good strategic move to guess E or maybe C on this question, and then move on).
(1) Definitely not enough info. For one thing we don't know about E, and we have no info about WHEN any of the other pilots can meet. Additionally, we still don't know about the stuff we didn't know about before we looked at (1).
(2) tells us that B and E can meet together starting at 10:30pm on any weekday. So that's two; but we don't know whether or not a third can join them. Insufficient.
(1) + (2)
We know from (1) that A and C can't meet together. So, out of that pair, only 1 is available to meet at any given time. But from (2), we know that B and E are "ONLY" available to meet starting at 10:30pm and not ending during the AM hours of any weekend day. Thus, B and E can ONLY meet Monday through Thursday beginning at 10:30 pm. If they meet at 10:30pm, the meeting will run 'til 12:30 am the next day. But from (1), we know that neither of A nor C can end any meeting during the AM hours of ANY weekday.
Thus, neither of A nor C can ever meet with either of B or E. And A can't meet with C. So, if you diagram it something like this
...........AxxxC
...........B.....D
you can see that you can't have the "horizontal block" AC, you can't have either of the "vertical blocks" AB or CD, and you can't have either of the "diagonal blocks" AD or BC. So, out of this quartet, that leaves B and D as the only pair whose meeting together hasn't been ruled out as a possibility; this doesn't meet that we know that B or D are for sure able to meet together.
We know from (2) that B and E are able to meet starting at 10:30pm on any weekday, so B and E are the only two pilots we know of that are for sure able to meet together at a certain time; we know for sure that A and C can't join them (B can't meet with either of A or C as discussed in the paragraph above) but whether D can join them (B and E that is), we cannot say. So, we don't know whether or not three of them can meet for two hours uninterrupted.
Choose (E).
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