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 a dedicated runner and runs 5 times a week; therefore, he will never run more than a 7 - minute mile.
○ 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.
○ andrew is the fastest runner on the team, so 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.

Explanation:

A counterexample to a statement using inductive reasoning (which generalizes from specific cases) is an instance that disproves the generalization. The original statement claims Andrew will always run a sub - 7 - minute mile. We need to find an option where Andrew runs more than 7 minutes.

• Option 1: Says he will never run more than 7 minutes, which supports the statement, not a counterexample.
• Option 2: Talks about his coach's belief and other runners, not about Andrew's mile time exceeding 7 minutes.
• Option 3: Says he will never run more than 7 minutes, supports the statement.
• Option 4: In the fifth race, due to conditions, his mile time is 8 minutes (more than 7), so this disproves the claim that he will always run a sub - 7 - minute mile.

Answer:

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.