ranvijay87 wrote:Of the 100 athletes at a soccer club , 40 play defense and 70 play midfield.if atleast
20 of the athletes play neither defense nor midfield , the no of athletes that play
both midfield and defense could be any no between
1.10 to 20
2.20 to 40
3.30 to 40
4.30 to 70
5.40 to 70.
[Moderator Edit: Moving to a relevant section]
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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