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? | + | 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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==Solution== | ==Solution== | ||
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<math>(2,2+2)\equiv (2,4)</math>. <math>4</math> isn't a prime, so this isn't a set of twin primes. | <math>(2,2+2)\equiv (2,4)</math>. <math>4</math> isn't a prime, so this isn't a set of twin primes. | ||
− | <math>(3,3+2)\equiv (3,5)</math>. <math>5</math> is a prime, so the answer is <math>\frac{3+5}{2}=4 | + | <math>(3,3+2)\equiv (3,5)</math>. <math>5</math> is a prime, so the answer is <math>\frac{3+5}{2}=4</math>. |
− | == | + | |
− | + | ==Cheap Solution== | |
+ | Note that <math>A</math> is the only answer choice offered, so you must choose it. | ||
− | {{iTest box|before=First | + | ==See Also== |
+ | {{iTest box|year=2007|before=First Question|num-a=2}} | ||
[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] |
Latest revision as of 11:33, 29 January 2021
Contents
[hide]Problem
A twin prime pair is a set of two primes such that is greater than . What is the arithmetic mean of the two primes in the smallest twin prime pair?
Solution
We consider the first few primes. . isn't a prime, so this isn't a set of twin primes.
. is a prime, so the answer is .
Cheap Solution
Note that is the only answer choice offered, so you must choose it.
See Also
2007 iTest (Problems, Answer Key) | ||
Preceded by: First Question |
Followed by: Problem 2 | |
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