Difference between revisions of "2007 iTest Problems/Problem 1"

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==Problem==
 
==Problem==
A twin prime pair is a set of two primes <math>(p, q)</math> such that <math>q</math> is <math>2</math> greater than <math>p</math>.  What is the arithmetic mean of the two primes in the smallest twin prime pair?  
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A twin prime pair is a set of two primes <math>(p, q)</math> such that <math>q</math> is <math>2</math> greater than <math>p</math>.  What is the arithmetic mean of the two primes in the smallest twin prime pair?
 
 
<math>\mathrm{(A)}\, 4</math>
 
  
 
==Solution==
 
==Solution==

Revision as of 13:57, 24 February 2020

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?

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 $\boxed{\mathrm{A}}$.

See Also

2007 iTest (Problems, Answer Key)
Preceded by:
First Question
Followed by:
Problem 2
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