HarveyS wrote:

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

Here is how you can think about it:

We are given the minimum value of "Neither" and we need to find the minimum and maximum value of "Both".

Total = A + B - Both + Neither

Both = 40 + 70 - 100 + Neither

Both = 10 + Neither

Minimum value of Neither is 20.

Maximum value of Neither will be obtained when "defense" circle in inside the "midfield" circle. So 100 - 70 = 30 would be Neither.

So minimum value of Both is 10+20 = 30 and maximum value is 10+30 = 40.

Answer (C)

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