Take a look at Section 2, Question 6 of the June 2007 LSAT. Don't bother reading the answer choices. The answer, as usual, is to be found in the argument itself. Read carefully. Read slowly. Read it twice if you have to. Go ahead, I'll be here when you come back.
You could probably diagram this question, but I think you'd be foolish if you did. The problem with diagramming is that you add a level of abstraction to your thinking, making it easy to misunderstand the argument and introduce silly mistakes. I end up doing a diagram for maybe one or two questions per test. (Basically, only when I'm in trouble and can't think of any other way to do it.) This isn't one of those times, because I already know why the argument is bullshit. The argument is bullshit because it has assumed (rather than stated) that the position of Executive Administrator is on the executive board.
When I say "assumed," what I mean is that the argument has left out a key piece of evidence. Here, the argument never specifically says that the position of Executive Administrator is an executive board position. Sure, it may sound like a board position. But that's not enough. The speaker here needs to specifically state that fact. If it's true, then I think the logic is pretty tight. There's a premise (i.e., stated evidence) that says nobody with a felony conviction can serve on the board. There's a premise that says Murray has a felony conviction. If it's also true that the Executive Administrator is on the executive board, then I would be forced to conclude that Murray can't be on the board.
I haven't even looked at the question yet, let alone the answer choices. But since I know what the argument is missing, I'm already 90% of the way to answering whatever the question may be.
The question here says "The argument's conclusion follows logically if which one of the following is assumed?" This is what's known as a Sufficient Assumption question. What it really means is "which one of the following would prove the conclusion of the argument?" ("Follows logically" simply means "is proven" on the LSAT.)
I love Sufficient Assumption questions, because the answers are really easy to predict. To prove the argument's conclusion, the correct answer simply must cover up the hole in the argument that I have discussed above. The correct answer must somehow connect the position of Executive Administrator to the executive board. Here are a few predictions for what the correct answer might be:
1) "The Executive Administrator is on the executive board." (clean and simple.)
2) "Any job Murray would apply for would be on the executive board." (backdoor, but it would work.)
3) "All jobs in the world are on the executive board." (overkill, but definitely sufficient.)
I think the correct answer is probably going to be something very similar to #1. But I'm not afraid of answers like #2 or #3 here, even though they might seem too strong. Some questions on the LSAT prefer strongly-stated answers. Sufficient Assumption questions fall into this category. It's okay if the correct answer goes overboard here, as long as it proves that Murray can't get the job. Let's look at the answer choices:
A) We were asked to prove that Murray is not eligible for the board. This answer choice could not be used to prove that Murray is eligible for the board, but that's not the same thing as proving that he is not eligible. Furthermore this answer doesn't connect the Executive Administrator position to the board. Let's keep looking.
B) Okay, this one would do it. It's not exactly what I predicted, but if this is true then Murray isn't eligible for the job, and that's what we need to prove. We know he is ineligible for the board because of the felony conviction. If the Executive Administrator position has the same requirements as the board, then Murray is out of luck. Mission accomplished. I am 99.9% certain this will be the correct answer. Still, I'll always quickly read the rest of the answer choices just in case.
C) This answer, if true, only makes it easier to get the job, not harder. We want to prove that Murray can't get the job. (Furthermore it is entirely irrelevant to Murray because he does have a bachelor's degree.) This answer is bad. Very bad.
D) Sure, and if your grandma had balls, she'd be your grandpa. Murray does have a felony conviction, so this answer is useless. (Furthermore, we wanted to prove that Murray can't get the job, and this answer choice could only be used to prove that he could get the job... If he didn't have the conviction, which he does.) This is a comedically bad answer, just like C.
E) No. The "duties" of the position are irrelevant. I suppose this answer choice strengthens the case that Murray shouldn't get the job. (If Murray was convicted of embezzlement, and this is an accounting position, then that would seem to be a strike against him.) But answer B proves that Murray can't get the job. We want to prove our case, not just strengthen it. So our answer is B.