Of the 100 athletes at a soccer club, 40 play defense and 60 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 Choose the correct choice from the following choices
A) 10 to 20 B) 10 to 40 C) 20 to 40 D) 30 to 70 E) 40 to 70
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 + 60 - {both} + {neither}   {both} = {neither} + 0   Since the least value of {neither} is given to be 20, then the least value of {both} is   20+0= 
<gadget id="calculator">  20+0</gadget>
<output>20</output>
20.Eliminate A and B.   Answer: 20 to 40.
<result>C</result>
Of the 100 athletes at a soccer club, 40 play defense and 60 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