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| − | == Problem ==
| + | #REDIRECT[[2003 AMC 12A Problems/Problem 8]] |
| − | What is the probability that a randomly drawn positive factor of <math>60</math> is less than <math>7</math>
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| − | <math> \mathrm{(A) \ } \frac{1}{10}\qquad \mathrm{(B) \ } \frac{1}{6}\qquad \mathrm{(C) \ } \frac{1}{4}\qquad \mathrm{(D) \ } \frac{1}{3}\qquad \mathrm{(E) \ } \frac{1}{2} </math>
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| − | == Solution ==
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| − | For a positive number <math>n</math> which is not a perfect square, exactly half of the positive factors will be less than <math>\sqrt{n}</math>.
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| − | Since <math>60</math> is not a perfect square, half of the positive factors of <math>60</math> will be less than <math>\sqrt{60}\approx 7.746</math>.
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| − | Clearly, there are no positive factors of <math>60</math> between <math>7</math> and <math>\sqrt{60}</math>.
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| − | Therefore half of the positive factors will be less than <math>7</math>.
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| − | So the answer is <math>\frac{1}{2} \Rightarrow E</math>.
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| − | == See Also ==
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| − | {{AMC10 box|year=2003|ab=A|num-b=7|num-a=9}}
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| − | [[Category:Introductory Number Theory Problems]] | |
