Self-study
Ann: All the campers at Camp Winnehatchee go to Tri-Cities High School.
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Misdirected Response
This question features a unique stem that doesn't fit cleanly into our common question types. I think it's best described as a misdirected response question. Misdirected responses are a common flaw pattern – one speaker will attempt to counter another, but will either ignore or misinterpret the position they're arguing against.
Quantifiers And Counterexamples
This question tests a straightforward sufficiency / necessity confusion, and the answer choices reward test takers who have a firm knowledge of quantifiers.
We can negate conditional claims by providing a counterexample. For instance, if I say "All my friends are pro basketball players," you could counter by saying "What about Phil? He is your friend, but he is not a pro basketball player. Phil's existence disproves my claim – it shows that not all my friends are pro basketball players.
Claim: Friend → Pro Bball
Valid Counter: PhilFriend and /Bball
That doesn't work the other way around, though. If you say "What about Devon? She is a pro basketball player, but she is not your friend," I can respond by saying "I know – I'm not saying I'm friends with every single pro basketball player…"
That's what's happening here. Bill's counterexample doesn't make sense as a response to Ann's claim – he's getting her conditional claim backward.
Claim: Winnehatchee → Tri-City
Valid Counter: Some studentsWinnehatchee and /Tri-City
Bill's Counter: Some studentsTri-City and /Winnehatchee
2.
Bill’s answer can be best █████████ ██ ███ ██████████ ████ ██ ███ ███████████ ███████ ██████ ██ ████ ████
a
most of the ███████ ██ ████ ████████ ████ ████ ████ ███████ █████ ████ ██████████
(A) gets the quantifier wrong. You can't counter "most" claims with a single counterexample. You don't even need to read the rest.
b
most Tri-Cities High ██████ ████████ ███ ███████ ██ ████ ████████████
(B) gets the quantifier wrong. You can't counter "most" claims with a single counterexample. You don't even need to read the rest, which is good because (B) matches the correct answer in all other respects.
c
some Tri-Cities High ██████ ████████ ████ █████████ ████ ████ ████████
(C) gets the quantifier wrong. You can't counter "some" claims with a single counterexample. You don't even need to read the rest.
d
all Tri-Cities High ██████ ████████ ██████ ██████ ████
(D) would be right if it said "attend camp Winnehatchee" instead of "attend summer camp." Summer camp is too broad; it includes Camp Lakemont, for example.
e
only campers at ████ ████████████ ███ ████████ ██ ██████████ ████ ██████
(E) expresses the backward version of Ann's claim, for which Bill's counterexample would make sense:
(E)'s Claim: Tri-City → Winnehatchee
Bill's Counter: Some studentsTri-City and /Winnehatchee