NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 16:14 It is currently 23 Apr 2024, 16:14
Decision Tracker
My Rewards
New posts
New comers' posts

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

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
HarveyS
Manager
Manager
Joined: 14 Jan 2013
Posts: 114
Own Kudos [?]: 1527 [18]
Given Kudos: 30
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE:Consulting (Consulting)
Send PM
Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink] New post   23 Mar 2014, 01:40
1
Kudos
17
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

70% (01:47) correct 30% (01:46) wrong based on 526 sessions
Hide Show timer Statistics
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
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618586 [6]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink] New post   23 Mar 2014, 05:33
5
Kudos
1
Bookmarks
Expert Reply
Mountain14 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

A. 10 to 20
B. 10 to 40
C. 30 to 40
D. 30 to 70
E. 40 to 70


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
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1562
Own Kudos [?]: 7207 [5]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink] New post   25 Jul 2014, 02:49
5
Kudos
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 7913 times ]

General Discussion
User avatar
haree87
Intern
Intern
Joined: 02 Jan 2015
Posts: 21
Own Kudos [?]: 35 [5]
Given Kudos: 15
Send PM
GMAT ToolKit User
Re: Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink] New post   12 Sep 2015, 00:34
5
Kudos
Mountain14 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

A. 10 to 20
B. 10 to 40
C. 30 to 40
D. 30 to 70
E. 40 to 70


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 7255 times ]

User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64882 [3]
Given Kudos: 426
Location: Pune, India
Send PM
Re: Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink] New post   09 Aug 2017, 04:46
3
Kudos
Expert Reply
HarveyS 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

A. 10 to 20
B. 10 to 40
C. 30 to 40
D. 30 to 70
E. 40 to 70


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
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18753
Own Kudos [?]: 22041 [1]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink] New post   03 Apr 2019, 18:08
1
Kudos
Expert Reply
HarveyS 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

A. 10 to 20
B. 10 to 40
C. 30 to 40
D. 30 to 70
E. 40 to 70


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
B
Malar95
Senior Manager
Senior Manager
Joined: 29 Oct 2023
Posts: 331
Own Kudos [?]: 162 [0]
Given Kudos: 11
Location: Malaysia
Send PM
Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink] New post   09 Jan 2024, 08:20
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
GMAT Club Bot
gmatclubot
Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink]
09 Jan 2024, 08:20
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions