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mathmath333

  • one year ago

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  1. mathmath333
    • one year ago
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    In a carrom board game competition, m boys and n girls (m > n > 1) of a school participate in which every student has to play exactly one game with every other student. Out of the total games played, it was found that in 221 games one player was a boy and the other player was a girl. Consider the following statements : statement 1.) The total number of students that participated in the competition is 30 statement 2.)The number of games in which both players were girls is 78 Which of the statements given above is/are correct? a.)1 only b.)2 only c.)Both 1 and 2 d.)Neither 1 nor 2

  2. mathmath333
    • one year ago
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    i have found both 1 and 2 are true

  3. mathmath333
    • one year ago
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    soln is 1.) 17 boys* 13 girls=221 2.) 13C2=78 but i am confused how did one arrive at this thinking with many possiblities

  4. phi
    • one year ago
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    I am thinking first boy plays against n girls, 2nd boy plays against n girls, etc we get mn games with 1 boy vs 1 girl thus mn= 221 this suggests we factor 221 guess what it factors into ??!

  5. mathmath333
    • one year ago
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    of course 221 has only 2 prime factors was this a trick question

  6. phi
    • one year ago
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    yes, especially if you have not memorized the larger primes (but computers come to the rescue!)

  7. mathmath333
    • one year ago
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    if one founds that the number of girls is 13 than it is easy to find 13C2=78

  8. phi
    • one year ago
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    yes, to solve this problem , you have to find that trick, i.e. figure out m*n= 221 and then notice that only 17 and 13 are factors of 221 (other than 1 and 221, and this one is excluded because both m and n > 1)

  9. mathmath333
    • one year ago
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    thnks so much

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