Of the 100 athletes at a soccer club, 40 play defense and 70

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BTGmoderatorLU: Moderator; Posts: 2550; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Apr 01, 2019 2:43 pm

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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

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Source: Beat The GMAT — Problem Solving | Mon Apr 01, 2019 2:43 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Wed Apr 03, 2019 3:04 am

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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swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Wed Apr 03, 2019 7:24 am

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 + 70 - {both} + {neither}
{both} = {neither} + 10.

Since the least value of {neither} is given to be 20, then the least value of {both} is 20+10=30. Eliminate A and B.

Therefore, the correct answer is __C__.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8151; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Apr 03, 2019 5:04 pm

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8151; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Apr 04, 2019 5:33 pm

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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