Tennis tournament logic

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Tennis tournament logic

by himu » Sun Nov 18, 2012 7:53 pm
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?


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.

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.

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.

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.

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.
Source: — Critical Reasoning |

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by Bill@VeritasPrep » Sun Nov 18, 2012 8:03 pm
The stimulus gives us a general if/then relationship, then follows with a specific example of the contrapositive.

If A (fifth-set tiebreak), then B (lower-ranked loses). If not-B (lower-ranked player wins), then not-A (no tiebreak).

A follows this structure:

If A (three pregnancies), then B (one set of twins). If not-B (more than one set of twins), then not-A (not exactly three pregnancies)
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by himu » Sun Nov 18, 2012 8:37 pm
Perfect Bill !
Thanks :)

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by Bill@VeritasPrep » Sun Nov 18, 2012 9:31 pm
You're welcome. Feel free to hit the 'thank' button if you'd like ;)

The other one I've seen people choose here is D, but it follows an A-->B, not A-->not B structure, which doesn't match (and is logically incorrect).
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