Hi MagicMeat,First, so we're working on the same thing. The question in the second half of your post, the one with the friends' recommendation and the "either Oshin or Reena, but not both" rule, is a different question from the one in this thread. The roles are swapped, the selection rule is inverted, and both statements are new. That modified version is the one you want explained, so that is what this is about.
Why it comes out to A.Two conditions govern the town they chose: it had to be recommended by the friends, and exactly one of the two had to have been there before. Now hold on to something the stem hands you for free. They
did make the trip, and the town they picked
did meet both conditions. You never have to prove that part for any particular town.
Then statement (1) puts Town F and Town J on the friends' list. Read that as the recommendations in full and the whole thing closes in one step:
- The town they visited was recommended.
- The recommended towns are F and J.
- So they went to F or to J.
- Both are among the four towns in the question.
The answer is yes. And notice you never had to settle
which of the two it was, because either way the answer to "did they visit one of these four towns" comes out the same. That is what makes statement (1) sufficient on its own, which is
A.
Where your reasoning slips. You said the condition "was not satisfied." It was satisfied - the stem guarantees it for whichever town they actually chose. What you cannot do from statement (1) is put a name to that town, and the elegance of this question is that you do not need to. Once the candidate list is down to F and J, naming it stops mattering.
Now the fair part of your objection. The phrase "Among the towns recommended by their friends were Town F and Town J" is carrying a lot of weight, and it does not carry it cleanly. Read strictly, "among ... were" tells you only that F and J are
on the list and leaves room for others. On that reading your instinct is right and the answer would be
E, because some fifth recommended town that exactly one of them had visited could exist, and they could have gone there instead. Nothing in the statements shuts that door.
So the intended reading is that F and J are the full set of recommendations, and that gives you
A. Your discomfort was worth having. It just lands on the wording rather than on the logic.
One thing worth keeping separate. The question at the top of this thread is not the same problem, and on its own terms its answer is
E: there the four towns are explicitly not the only candidates, so a fifth town is always live. Review the two side by side and you will see the modification is precisely what removes that escape route.
Answer: A for the modified version you posted. The question in this thread stays
E.
MagicMeat
I saw this on egmat as a modified of the same question. the answer as per egmat was A. But i believe it should be E as the condition that " recommended by their close friends and that either Oshin or Reena, but not both, had visited before" was not satisfiedLast summer, as with every summer, Oshin and Reena made exactly one long trip together. However, unlike previous years, this time, they decided to visit a town that was recommended by their close friends and that either Oshin or Reena, but not both, had visited before. Did Oshin and Reena visit one of these four towns last summer? Oshin had visited Town F and Town G before, while Reena had never visited Town J or Town K.(1) Among the towns recommended by their friends were Town F and Town J.(2) Reena prefers visiting towns that Oshin has already explored to have a familiar guide.