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Of the 100 athletes at a soccer club, 40 play defense and 70 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between
  • a)
    10 to 20
  • b)
    10 to 40
  • c)
    30 to 40
  • d)
    30 to 70
  • e)
    40 to 70
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Of the 100 athletes at a soccer club, 40 play defense and 70 play midf...
First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40. Eliminate D and E.
{Total} = {defense} + {midfield} - {both} + {neither}
100 = 40 + 70 - {both} + {neither}
{both} = {neither} + 10.
Since the least value of {neither} is given to be 20, then the least value of {both} is 20 + 10 = 30. Eliminate A and B.
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Of the 100 athletes at a soccer club, 40 play defense and 70 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number betweena)10 to 20b)10 to 40c)30 to 40d)30 to 70e)40 to 70Correct answer is option 'C'. Can you explain this answer?
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