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Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The integer $n$ is such that $1 < n < 99$ . $P$ is the difference between 1 and $n$ , $Q$ is the difference between 99 and $n$ , and $R$ is the difference between $P$ and $Q$ . For how many values of $n$ is $R$ a prime number?

(A) $0$ (B) $2$ (C) $4$ (D) $8$ (E) $99$

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