Question

1. sammy sells cars. last week, he sold 6 used cars to 6 different customers. each person he sold a used car to was under the age of 35. this week, he sold a new car to a couple in their 50s. sammy determined that only customers who are 35 and younger buy used cars. what is a counterexample to sammys conjecture?

a customer who is 38 years old buys a used car.
a customer who is 38 years old buys a new car.
a customer who is 30 years old buys a used car.
a customer who is 62 years old buys a new car.

Explanation:

A counterexample to a conjecture is an example that disproves it. Sammy's conjecture is that only customers 35 and younger buy used cars. To counter this, we need an example of a customer over 35 buying a used car.

• Option 1: A 38 - year - old (over 35) buying a used car directly contradicts the conjecture.
• Option 2: A 38 - year - old buying a new car doesn't relate to the conjecture about used cars.
• Option 3: A 30 - year - old (35 or younger) buying a used car supports the conjecture, not counter it.
• Option 4: A 62 - year - old buying a new car also doesn't relate to the conjecture about used cars.

Answer:

A. A customer who is 38 years old buys a used car.