2019 AMC 10B Problem 2

Problem 2 of 25EasierNumber Theory

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?

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Solution

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 .

Concepts: counterexample · prime

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