by ohthatpatrick Sat Jan 11, 2014 6:25 pm
It is quite confusing when you hear "at least one of which must be on the team".
In general, how do you test MUST BE TRUE answer choices?
Do you see if the answer choice is possible or do you see if REFUTING the answer choice is possible?
The latter. Testing to see if an answer choice is possible only tells you that something COULD be true.
In order to know whether it MUST be true, you have to try to 'break' the answer, i.e., come up with a counterexample.
Eliminating answers on Must Be True is kinda like being a snotty, disagreeable teenager.
If an answer choice says that "the earliest F can go is 3"
we think, "Nuh-uh. F can go in 2."
If an answer choice says that "there are at most two people in the Finance group",
we think, "Nuh-uh, it's possible for three people to be in the Finance group".
So when they say "at least one of these two guys must be IN",
we think, "Nuh-uh, it's possible that _______
... it's possible that they're both out.
So we should be analyzing these answer choices by asking ourselves, "Is it possible for BOTH of these guys to be OUT?"
If both people can be OUT together, we'll eliminate the answer.
If both people could NEVER be out together, that will be the correct answer. It must be true that at least one of them is IN.
(A) Can O and S both be OUT? Sure. Neither ~O nor ~S trigger any rules.
(B) Can O and W both be OUT? Sure. Neither ~O nor ~W trigger any rules.
C) Can P and S both be OUT? Sure, in fact we even have a rule that says ~P --> ~S.
(D) Can T and Y both be OUT? No, because of the chain reactions of the rules and the fact that we need 4 people IN.
Rule 3 says that ~Y --> ~W.
Rule 2 says that ~T --> ~S.
Okay, we'll our OUT column has a maximum of four spots. Those spots are now filled.
If Y, W, T, and S are all OUT, then we need to put the other four IN to satisfy the minimum of four IN.
That means that M, P, O, and Z are all IN. But that doesn't work. When M is IN, P and O are OUT.
Since it was impossible for T and Y to both be OUT, (D) is correct to say that at least one of them must be IN.
(E) Can Y and Z both be OUT? Sure. ~Y -> ~W, but Z doesn't trigger any rules. We could have Y, W, Z, and M OUT and have O, P, S, and T IN.
Hope this helps.