Understanding the argument -
Ann: All the campers at Camp Winnehatchee go to Tri-Cities High School - meaning anyone camping at CW goes to TC High School.
Bill: That‟s not true. Some Tri-Cities students are campers at Camp Lakemont. - Bill has conveniently reversed what Ann said. Bill interpreted that Ann said, "All who attend TC High School only attend CW camp. And that's what he negated. His negated conclusion is "not all who go to TC high school go to CW camp." He substantiates his misinterpreted conclusion by saying, "Some, which can be at least two students, are campers at camp L."
We need to look for an assumption for his conclusion: "Not all who go to TC high school go to CW camp." For this conclusion, we need to assume, need minimum condition, or need a missing premise saying (his misinterpreted understanding of what Ann said), "All who go to TC High School only go to CW camp," or "Only campers at CW are students of TC high school." This is "only if conditional," meaning if you are a student of TC High School, you attend CW camp, meaning "all students of TC High School go to CW camp. This is what option E states, but the author has packaged the answer in the "only if" conditional to make it more challenging to figure out the answer.
A key takeaway from this question is his wrong interpretation (All who attend TC High School only attend CW camp) + wrong conclusion (not all who go to TC High School go to CW camp); the assumption or missing premise is his wrong interpretation which is "All who attend TC High School only attend CW camp." Yes, the language of E is in the form of "only if conditional," but it necessarily means all the students of TC high school attend the CW camp.
Option Elimination - This option is checking the sufficient condition for Bill's argument to hold (Question stem - Bill's answer can be best explained on the assumption that he has interpreted Ann's remark to mean that):
(A) most of the campers at Camp Lakemont come from high schools other than Tri-Cities - schools other than TC are out of scope.
(B) most Tri-Cities High School students are campers at Camp Winnehatchee - a more straightforward interpretation would be. Say most is "99.99" of TC High schools students are campera at CW. It's going in a direction opposite to what Bill says. He concludes, saying, "Some Tri-Cities students are campers at Camp Lakemont." Opposite of what we need.
Or this can mean some can also be campers at other camps. We already know this from Bill's argument as he said the same thing by saying, "Some Tri-Cities students are campers at Camp Lakemont." But what is the scope of the argument here? Do we need to find an assumption for the misinterpreted conclusion, which is "not all who go to TC high school go to CW camp," or to strengthen the conclusion "not all who go to TC high school go to CW camp"? Our job here is to find an assumption and not a strengthener.
(C) some Tri-Cities High School students have withdrawn from Camp Lakemont - Bill's conclusion is about the attendance of TC students at Camp L and not about the withdrawal, which is out of scope.
(D) all Tri-Cities High School students have withdrawn from Camp Lakemont - same issue as C with extrapolating from some" to "all." Out of scope.
(E) only campers at Camp Winnehatchee are students at Tri-Cities High School - Option E is tricky. It's a "necessary" conditional. Only if X, then Y.
Example -
Only if you study hard will you pass the exam (Only if you X, then Y). This means Y implies X, and Not X implies not Y.
Means
if you pass the exam, then you must have studied hard.
If you do not study hard, you don't pass the exam.
Makes sense? If yes, then proceed; otherwise, relook at the conditional.
So, the implication of option E (only campers at Camp Winnehatchee are students at Tri-Cities High School) is:
If you are a student at TC High School, you camp at CW, meaning "all students of TC High School camp at CW."
This is precisely what Bill mistakenly took as Ann's conclusion: the missing premise and our assumption or the sufficient condition for the argument to hold.