Problem Solving

BTGmoderatorLU wrote:Source: Veritas Prep

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

The OA is C

Given that there are 100 athletes at a soccer club, and at least 20 of the athletes play neither midfield nor defense, we have less than 80 athletes who play either midfield or defense or both.

Thus, 80 > 40 + 70 - both

Thus, both > 30

Since the value of both cannot be greater than 40, we have 40 > both > 30.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Veritas Prep

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

The OA is C

we can use the formula for overlapping sets:

Total = Midfield + Defense - Both + Neither

Now, using the least number of athletes who play neither position (20 players), we have:

100 = 70 + 40 - x + 20

100 = 130 - x

x = 30

So 30 is the least number of athletes who play both positions. However, the number of athletes who play both positions can't exceed the number of athletes who play defense. Therefore, the greatest number of athletes who play both positions is 40.

Answer: C

BTGmoderatorLU wrote:Source: Veritas Prep

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

The OA is C

We can use the formula for overlapping sets:

Total = Midfield + Defense - Both + Neither

Now, using the least number of athletes who play neither position (20 players), we have:

100 = 70 + 40 - x + 20

100 = 130 - x

x = 30

So 30 is the least number of athletes who play both positions. However, the number of athletes who play both positions can't exceed the number of athletes who play defense. Therefore, the greatest number of athletes who play both positions is 40.

Answer: C