CSASHISHPANDAY 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
10 to 20
10 to 40
30 to 40
30 to 70
40 to 70
Total = Defense + Midfield - Both + Neither.
The big idea is to SUBTRACT the overlap.
When we count the total number who play defense and the total number who play midfield, the OVERLAP -- everyone who plays BOTH positions -- is counted TWICE.
Thus, the athletes who play BOTH positions must be subtracted from the total so that they are not double-counted.
In the equation above:
Total = 100.
Defense = 40.
Midfield = 70.
Both = B.
Neither = N.
Plugging these values into the equation:
100 = 40 + 70 - B + N
-10 = -B + N
B = N + 10.
To minimize B, we need to minimize N.
It is given that the minimum value of N is 20:
B = N + 10 = 20 + 10 = 30.
Since the minimum value of B is 30, eliminate A, B and E.
In C, the maximum value of B is 40.
In D, the maximum value of B is 70.
Since only 40 athletes play defense, it is not possible that 70 athletes play both positions.
Eliminate D.
The correct answer is
C.
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