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

(Problem)
(Alternate Solution)
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<math>(3,3+2)\equiv (3,5)</math>. <math>5</math> is a prime, so the answer is <math>\frac{3+5}{2}=4\Rightarrow \boxed{\mathrm{A}}</math>.
 
<math>(3,3+2)\equiv (3,5)</math>. <math>5</math> is a prime, so the answer is <math>\frac{3+5}{2}=4\Rightarrow \boxed{\mathrm{A}}</math>.
===Alternate Solution===
 
Seeing as <math>A</math> is the only choice, we determine that the answer is <math>\boxed{\mathrm{A}}</math>.
 
 
 
==See Also==
 
==See Also==
 
{{iTest box|year=2007|before=First Question|num-a=2}}
 
{{iTest box|year=2007|before=First Question|num-a=2}}
  
 
[[Category:Introductory Number Theory Problems]]
 
[[Category:Introductory Number Theory Problems]]

Revision as of 14:57, 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 $\frac{3+5}{2}=4\Rightarrow \boxed{\mathrm{A}}$.

See Also

2007 iTest (Problems, Answer Key)
Preceded by:
First Question
Followed by:
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 TB1 TB2 TB3 TB4