tennis logic

[jigar24]

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?
1) 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.

2) 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.

3) 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.

4) 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.

5) 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.








OA- (1)

My question - why is (4) wrong??

[thesubjunctive]

The structure of the argument is

If, A [in a tennis tournament, a match reaches a fifth-set tiebreak,] then B [the lower-ranked player always loses the tiebreak (and, therefore, the match)]. If NOT B [Rafael, the second-ranked player, wins a tournament by beating Roger, the top-ranked player,] then NOT A [then the match must not have included a fifth-set tiebreak.]

So, we are looking for a structure similar to If A then B. If not B, then not A.

4) If A [a student is in the top 10% of her class], then B [she will earn a college scholarship.] Not A [Anna is not in the top 10% of her class], then not B [so she will not earn a scholarship.]

Structure: If A then B. Not A then not B. Not what we are looking for.

Answer 1 most closely matches the structure If A then B. If not B, then not A.

[Ben Ku]

Thanks, thesubjunctive. Good explanation.

[aakashg.0]

EDITED

D is wrong because

The logic is if A, B. If not B, not A. (4) is If not A, not B.

(1) is If A (pregnant three times) then B (one set of twins). Jennifer = not B (two sets of twins), so not A.

[jnelson0612]

Thanks, everyone!