2019 AMC 12B Problem 2

Problem 2 of 25EasierNumber Theory Logic

Consider the statement, “If

n

is not prime, then

n-2

is prime.” Which of the following values of

n

is a counterexample to this statement?

Show solution

Solution

A counterexample needs

n

not prime (so the hypothesis holds) and

n-2

not prime (so the conclusion fails). Among the choices,

27

is not prime and

27-2=25

is not prime. The primes

11

and

19

fail the hypothesis, and

15-2=13,

21-2=19

are prime. Thus, E is the correct answer.

Tagged: counterexample · prime