2019 AMC 10B Problem 2

Attempt Problem 2 of the 2019 AMC 10B 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 10B 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 must make the hypothesis true and conclusion false

Check only choices where

n

is not prime

We need

n

to not be prime, so

n

can only be

15,21,27.

Then,

n-2

must be not prime, leaving just

27.

Thus, the answer is E .

Problem 2 in other years