2007 iTest Problems/Problem 1

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Problem

A twin prime pair is a set of two primes $(p, q)$ such that $q$ is $2$ greater than $p$ . What is the arithmetic mean of the two primes in the smallest twin prime pair?

$\mathrm{(A)}\, 4$

Solution

We consider the first few primes. $(2,2+2)\equiv (2,4)$ . $4$ isn't a prime, so this isn't a set of twin primes.

$(3,3+2)\equiv (3,5)$ . $5$ is a prime, so the answer is $\frac{3+5}{2}=4\Rightarrow \boxed{\mathrm{A}}$ .

Alternate Solution

Seeing as $A$ is the only choice, we determine that the answer is $\boxed{\mathrm{A}}$ .

2007 iTest (Problems)
Preceded by: First Question	Followed by: Problem 2
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2007 iTest Problems/Problem 1

From AoPSWiki

Contents

Problem

Solution

Alternate Solution

See Also