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

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2019 AMC 12B Problem 2

Below is the professionally curated solution for Problem 2 of the 2019 AMC 12B, 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.

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Concepts:counterexample prime

Difficulty rating: 990

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?

$11$

$15$

$19$

$21$

$27$

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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