Question

1. read the following statement, which uses inductive reasoning.

andrew runs cross - country for his high school. he ran a sub - 7 - minute mile (meaning it took him 7 minutes or less to run his mile) for his first three races. andrew will run a sub - 7 - minute mile for every race he runs this cross - country season.
which of the following is a counterexample to this statement?
andrew is the fastest runner on the team, so he will never run more than a 7 - minute mile.
andrew is a dedicated runner and runs 5 times a week; therefore, he will never run more than a 7 - minute mile.
the fifth race of the season, the cross - country runners had to run during a rainstorm and muddy conditions. due to the conditions, andrews mile time increased to 8 - minute - miles.
andrews coach believes he is the fastest runner in the state. he has trained other runners that are fast, but none of them have been as dedicated as andrew.

Explanation:

A counterexample to the statement (Andrew will run a sub - 7 - minute mile for every race this season) should be a situation where Andrew runs a mile that is not sub - 7 - minute (i.e., more than 7 minutes) in a race this season.

• The first option says he will never run more than 7 - minute mile, which supports the original statement, not counter it.
• The second option also says he will never run more than 7 - minute mile, supporting the statement.
• The third option describes a race (the fifth race of the season) where due to conditions, his mile time was 8 minutes (more than 7 minutes), so this is a case where he did not run a sub - 7 - minute mile in a race this season, thus a counterexample.
• The fourth option is about his coach's belief and his dedication, not about his race time, so it is not relevant to being a counterexample.

Answer:

C. The fifth race of the season, the cross - country runners had to run during a rainstorm and muddy conditions. Due to the conditions, Andrew's mile time increased to 8 - minute - miles.