2019 AMC 12B Problem 2

Attempt Problem 2 of the 2019 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2019 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

11

15

19

21

27

A counterexample makes the hypothesis true but the conclusion false

Look for

n

that is not prime while

n-2

is also not prime

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.

Problem 2 in other years