Last visit was: 15 Sep 2026, 10:01 It is currently 15 Sep 2026, 10:01
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
HarveyS
User avatar
Joined: 14 Jan 2013
Last visit: 25 Apr 2017
Posts: 112
Own Kudos:
1,796
 [22]
Given Kudos: 30
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE:Consulting (Consulting)
Posts: 112
Kudos: 1,796
 [22]
Of the 100 athletes at a soccer club, 40 play defense and 70 23 Mar 2014, 01:40
1
Kudos
Add Kudos
21
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

72% (01:47) correct 28% (01:47) wrong based on 621 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 15 Sep 2026
Posts: 113,537
Own Kudos:
841,460
 [6]
Given Kudos: 111,543
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,537
Kudos: 841,460
 [6]
Of the 100 athletes at a soccer club, 40 play defense and 70 23 Mar 2014, 05:33
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Mountain14
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
Show more

First of all 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.

Answer: C.
avatar
PareshGmat
avatar
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Own Kudos:
8,439
 [5]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
Kudos: 8,439
 [5]
Of the 100 athletes at a soccer club, 40 play defense and 70 25 Jul 2014, 02:49
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Refer diagram below

We require to find the shaded region

Setting up the equation

40 + 70-x + 20 = 100

x = 30

For defence = 40; the maximum value for which x can reach is also 40

Range = 30 to 40

Answer = C
Attachments

foot.png
foot.png [ 4.77 KiB | Viewed 9971 times ]

General Discussion
User avatar
haree87
User avatar
Joined: 02 Jan 2015
Last visit: 31 Jan 2016
Posts: 21
Own Kudos:
39
 [5]
Given Kudos: 15
Posts: 21
Kudos: 39
 [5]
Of the 100 athletes at a soccer club, 40 play defense and 70 12 Sep 2015, 00:34
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Mountain14
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
Show more

Fill the attached table and ull get the answer in less than a min

Since max number of athletes who can play defense s only 40, after filling the table u can conclude that the (c) 30 to 40 is the answer
Attachments

Screenshot_2015-09-12-13-01-11.png
Screenshot_2015-09-12-13-01-11.png [ 72.94 KiB | Viewed 9152 times ]

User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 15 Sep 2026
Posts: 16,655
Own Kudos:
81,346
 [3]
Given Kudos: 492
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,655
Kudos: 81,346
 [3]
Of the 100 athletes at a soccer club, 40 play defense and 70 09 Aug 2017, 04:46
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarveyS
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
Show more

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)
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 15 Sep 2026
Posts: 22,740
Own Kudos:
26,982
 [1]
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,740
Kudos: 26,982
 [1]
Of the 100 athletes at a soccer club, 40 play defense and 70 03 Apr 2019, 18:08
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarveyS
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
Show more

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
User avatar
Malar95
User avatar
Joined: 29 Oct 2023
Last visit: 13 Jun 2024
Posts: 328
Own Kudos:
170
Given Kudos: 11
Location: Malaysia
Posts: 328
Kudos: 170
Of the 100 athletes at a soccer club, 40 play defense and 70 09 Jan 2024, 08:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
https://gmatclub.com/forum/of-the-400-m ... 23692.html
Same technique as Bunuel's Table Matrix here.
Just be aware of the constraint that the max value can be 40 instead of 70
Moderator:
Bunuel
Math Expert
113537 posts