IEsailor wrote:
If, in a tennis tournament, a match reaches a fifth-set tiebreak, the lower-ranked player always loses the tiebreak (and, therefore, the match). If Rafael, the second-ranked player, wins a tournament by beating Roger, the top-ranked player, then the match must not have included a fifth-set tiebreak.
Which of the following arguments most closely mimics the reasoning used in the above argument?
(A) If a woman with a family history of twins gets pregnant three times, she will have one set of twins. Jennifer, who falls into this category, had two sets of twins, so she must not have gotten pregnant exactly three times.
(B) If a salesman sells more product than anyone else in a calendar year, then he will earn an all-expenses-paid vacation. Joe earned an all-expense-paid vacation, so he must have sold more product than anyone else for the year.
(C) A newspaper can charge a 50% premium for ads if its circulation surpasses 100,000; if the circulation does not pass 100,000, therefore, the newspaper can't charge any kind of premium for ads.
(D) If a student is in the top 10% of her class, she will earn a college scholarship. Anna is not in the top 10% of her class, so she will not earn a scholarship.
(E) All of the players on a football team receive a cash bonus if the team wins the Super Bowl. If quarterback Tom Brady earned a cash bonus last year, he must have been a member of the winning Super Bowl team.
OFFICIAL EXPLANATION
On a "
mimic the argument" question, it's useful to use logic notation to understand the flow of the argument. In this case, we're told that
IF A happens (a match reaches a fifth-set tiebreak),
THEN B will definitely happen (the lower-ranked player loses). Standard logic rules tell us that, when given "
If A, then B," the only definite conclusion we can draw is "
If not B, then not A." In other words, if A always leads to B, and B doesn't happen, then A can't have happened either. The second sentence of the argument shows this principle: If not B (the lower-ranked player doesn't lose), then not A (there wasn't a fifth-set tiebreak). So we need to find another argument that follows this pattern:
If A, then B; if not B, then not A.
(A) CORRECT. If A (a woman with a family history of twins gets pregnant 3 times), then B (she will have 1 set of twins). Note that these numbers are precise: if she gets pregnant exactly three times, she will have exactly one set of twins. If not B (a woman with a family history of twins has 2 sets of twins - that is, not 1), then not A (she must have gotten pregnant either fewer than 3 times or more than 3 times - that is, not exactly 3 times).
(B) If A (a salesman sells more product than anyone else), then B (he will earn an all-expenses-paid vacation). If B (Joe earned the trip), then A (he must have sold more than anyone else). We can see why logic rules do not include "if B, then A" as a logical conclusion: A may always lead to B, but B does not necessarily have to lead to A. There may be other ways to earn the trip besides selling more than anyone else.
(C) If A (a newspaper's circulation surpasses 100,000), then B (the newspaper can charge a 50% premium). If not A (the circulation doesn't surpass 100,000), then not C (the newspaper cannot charge any premium). The final assertion here does not match the initial A / B argument We know nothing about any other premium the newspaper might charge; we are only given information about charging a 50% premium.
(D) If A (a student is in the top 10% of the class), then B (she will earn a scholarship). If not A (Anna is not in the top 10%), then not B (she won't earn a scholarship). We can see why logic rules do not include "if not A, then not B" as a logical conclusion: A may always lead to B, but it doesn't have to be the only way to reach B. There may be other ways to earn a scholarship besides being in the top 10% of the class.
(E) If A (the team wins the Super Bowl), then B (the players receive a bonus). If not A (a player was not on the winning team), then not B (the player won't receive a bonus). We can see why logic rules do not include "if not A, then not B" as a logical conclusion: A may always lead to B, but it doesn't have to be the only way to reach B. There may be other ways to earn a bonus besides winning the Super Bowl.
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