Question

All the high schools in a large school district are involved in a fundraiser selling T-shirts. Which of the choices below is logically equivalent to the statement “No school bigger than Euclid HS sold more T-shirts than Euclid HS”?

All schools smaller than Euclid HS sold fewer T-shirts than Euclid HS.

No school that sold more T-shirts than Euclid HS is bigger than Euclid HS.

All schools bigger than Euclid HS sold fewer T-shirts than Euclid HS.

All schools that sold fewer T-shirts than Euclid HS are smaller than Euclid HS.

All schools smaller than Euclid HS sold more T-shirts than Euclid HS.

Answer: B

Concepts:logical deduction

Difficulty rating: 900

Solution:

The statement says: if a school is bigger than Euclid HS, then it did not sell more T-shirts than Euclid HS. Its contrapositive is: if a school sold more T-shirts than Euclid HS, then it is not bigger than Euclid HS. This is exactly choice B . Choice C is stronger than the original statement because it rules out a bigger school selling the same number of T-shirts.

Thus, the answer is B .

2022 AMC 10B Problem 11

Answer: B

Difficulty rating: 900

Solution:

Problem 11 in Other Years