Any person who scores poorly on the GMAT will not get into business sc

Official Explanation

Let’s start by symbolizing the argument. Symbolize the phrase “will get into business school” as S.* Next, symbolize the phrase “he bribes an admission officer” as B. Finally, symbolize the phrase “has a relative on the board of regents” as R. Substituting the symbols into the argument, we get the following diagram:

~(B or R)<—>~S

which simplifies to

(B or R)<—>S

(Note: We’ll add the phrase “any person who scored poorly on the GMAT” to the diagram later.)

We now use this diagram to analyze each of the answer-choices. As for choice (A), from ~S we can conclude, by applying the contrapositive to the diagram, ~(B or R). From DeMorgan’s laws, we know that this is equivalent to ~B & ~R. This is the premise of (A). That is, (A) is a valid argument by contraposition. This eliminates (A).

Since choice (B) affirms S, we know from the diagram that B or R must be true. But choice (B) denies R. So from the meaning of “or,” we know that B must be true. This is the conclusion of choice (B). Hence choice (B) is a valid deduction. This eliminates choice (B).

For simplicity we did not diagram the entire argument. But for choice (C), we need to complete the diagram. The premise of the argument is “any person who scores poorly on the GMAT.” This clause can be reworded as “If a person does poorly on the GMAT,” which can be symbolized as P. Affixing this to the original diagram gives

P—>[(B or R)<—>S].

Recall that if the premise of an if-then statement is true then the conclusion must be true as well. But if the premise is false, then we cannot determine whether the conclusion is true or false. Now (C) negates the premise, ~P. So its conclusion—that a person will get into business school, S—is a non sequitur. Hence

(C) is the answer.