BdMO National Junior 2010/3
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- Posts:1007
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One day Tom was playing with numbers.He wrote $11$ fractions using all natural numbers from $1$ to $22$ exactly once-either as numerator or as denomator.How many of these fractions ,at most,are integers?
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: BdMO National Junior 2010/3
Answer:$\fbox {10}$
Solution:
a fraction with prime number as denomator and numerator can never be a integer.
Integers are:
\[\dfrac {19}{1}\]
\[\dfrac {14}{2}\]
\[\dfrac {6}{3}\]
\[\dfrac {12}{4}\]
\[\dfrac {15}{5}\]
\[\dfrac {21}{7}\]
\[\dfrac {16}{8}\]
\[\dfrac {18}{9}\]
\[\dfrac {20}{10}\]
\[\dfrac {22}{11}\]
Not integer
\[\dfrac {13}{17}\]
Solution:
a fraction with prime number as denomator and numerator can never be a integer.
Integers are:
\[\dfrac {19}{1}\]
\[\dfrac {14}{2}\]
\[\dfrac {6}{3}\]
\[\dfrac {12}{4}\]
\[\dfrac {15}{5}\]
\[\dfrac {21}{7}\]
\[\dfrac {16}{8}\]
\[\dfrac {18}{9}\]
\[\dfrac {20}{10}\]
\[\dfrac {22}{11}\]
Not integer
\[\dfrac {13}{17}\]