2019 AMC 12B Problem 2 — Solution | LIVE by Po-Shen Loh

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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).

2.

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?

$11$

$15$

$19$

$21$

$27$

Answer: E

Concepts:counterexample prime

Difficulty rating: 990

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.

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