It is currently 13 Dec 2017, 20:46

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

There are 150 students at Seward High School. 66 students

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 31 May 2010
Posts: 94

Kudos [?]: 48 [0], given: 25

Reviews Badge
There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 14 Dec 2010, 06:23
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (01:28) correct 27% (02:04) wrong based on 408 sessions

HideShow timer Statistics

There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?

A. 0
B. 27
C. 30
D. 99
E. 78
[Reveal] Spoiler: OA

_________________

Kudos if any of my post helps you !!!

Kudos [?]: 48 [0], given: 25

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42598

Kudos [?]: 135563 [4], given: 12699

Re: Venn Diagram [#permalink]

Show Tags

New post 14 Dec 2010, 06:58
4
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
saurabhgoel wrote:
There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?
A) 0
B) 27
C) 30
D) 99
E) 78


Please help to understand the approach to tackle the venn diagram problems !!!


150 = {baseball} + {basketball} + {soccer} - {exactly 2 sports} - 2*{exactly 3 sports} + {none of the ports}:

150 = 66 + 45 + 42 - 27 - 2*3 + {none of the ports} --> {none of the ports}=30

Answer: C.

Look at the diagram:
Attachment:
untitled.PNG
untitled.PNG [ 9.43 KiB | Viewed 10734 times ]
When we sum {baseball} + {basketball} + {soccer} we count students who play exactly 2 ports (yellow section) twice, so to get rid of double counting we are subtracting {exactly 2 sports} once.

Similarly when we sum {baseball} + {basketball} + {soccer} we count students who play exactly 3 ports (blue section) thrice (as it is the portion of all three groups), so to count this group only once we are subtracting 2*{exactly 3 sports}.

For more on this check: formulae-for-3-overlapping-sets-69014.html#p729340

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135563 [4], given: 12699

Manager
Manager
User avatar
Joined: 07 Jan 2010
Posts: 143

Kudos [?]: 97 [0], given: 57

Location: So. CA
WE 1: 2 IT
WE 2: 4 Software Analyst
Re: Venn Diagram [#permalink]

Show Tags

New post 15 Dec 2010, 09:22
great explanation using venn diagram +1

Kudos [?]: 97 [0], given: 57

Manager
Manager
avatar
Joined: 19 Apr 2010
Posts: 207

Kudos [?]: 90 [0], given: 28

Schools: ISB, HEC, Said
Re: Venn Diagram [#permalink]

Show Tags

New post 16 Dec 2010, 00:49
Bunuel can we expect 3 overlapping set question on GMAT and are we supposed to know the formula.

Kudos [?]: 90 [0], given: 28

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42598

Kudos [?]: 135563 [0], given: 12699

Re: Venn Diagram [#permalink]

Show Tags

New post 16 Dec 2010, 04:24
prashantbacchewar wrote:
Bunuel can we expect 3 overlapping set question on GMAT and are we supposed to know the formula.


I've seen several GMAT questions on 3 overlapping sets, so you should understand the concept behind such kind of problems. Check this for more: formulae-for-3-overlapping-sets-69014.html#p729340
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135563 [0], given: 12699

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42598

Kudos [?]: 135563 [0], given: 12699

Re: There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 11 Jun 2013, 07:24
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135563 [0], given: 12699

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14854

Kudos [?]: 287 [0], given: 0

Premium Member
Re: There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 12 May 2017, 07:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 287 [0], given: 0

Manager
Manager
avatar
B
Joined: 08 Jun 2017
Posts: 71

Kudos [?]: 1 [0], given: 24

Re: There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 25 Jul 2017, 00:25
Hi you try doing question 203 in OG 17 the same way? there the 2*aandband c is not working Bunuel

Kudos [?]: 1 [0], given: 24

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42598

Kudos [?]: 135563 [0], given: 12699

Re: There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 25 Jul 2017, 00:32

Kudos [?]: 135563 [0], given: 12699

Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 597

Kudos [?]: 180 [0], given: 136

GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 25 Jul 2017, 00:38
saurabhgoel wrote:
There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?

A. 0
B. 27
C. 30
D. 99
E. 78


150 = 66+45+42 - 27 - 6 + x
x= 30

C
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Kudos [?]: 180 [0], given: 136

Manager
Manager
avatar
B
Joined: 08 Jun 2017
Posts: 71

Kudos [?]: 1 [0], given: 24

Re: There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 25 Jul 2017, 00:52
Hi Bunuel thanks a lot can question 132 be tackled the same way?

Kudos [?]: 1 [0], given: 24

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42598

Kudos [?]: 135563 [0], given: 12699

Re: There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 25 Jul 2017, 00:56

Kudos [?]: 135563 [0], given: 12699

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1940

Kudos [?]: 1017 [0], given: 3

Location: United States (CA)
Re: There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 26 Jul 2017, 15:33
saurabhgoel wrote:
There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?

A. 0
B. 27
C. 30
D. 99
E. 78


We can create the following equation:

Total students = # who play baseball + # who play basketball + # who play soccer - # who play exactly two - 2(# who play all 3) + # who play neither

150 = 66 + 45 + 42 - 27 - 2(3) + n

150 = 120 + n

n = 30

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1017 [0], given: 3

Intern
Intern
avatar
B
Joined: 22 Jun 2017
Posts: 6

Kudos [?]: 0 [0], given: 13

Re: There are 150 students at Seward High School. 66 students [#permalink]

Show Tags

New post 11 Aug 2017, 18:28
Bunuel wrote:
saurabhgoel wrote:
There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?
A) 0
B) 27
C) 30
D) 99
E) 78


Please help to understand the approach to tackle the venn diagram problems !!!


150 = {baseball} + {basketball} + {soccer} - {exactly 2 sports} - 2*{exactly 3 sports} + {none of the ports}:

150 = 66 + 45 + 42 - 27 - 2*3 + {none of the ports} --> {none of the ports}=30

Answer: C.

Look at the diagram:
Attachment:
untitled.PNG
When we sum {baseball} + {basketball} + {soccer} we count students who play exactly 2 ports (yellow section) twice, so to get rid of double counting we are subtracting {exactly 2 sports} once.

Similarly when we sum {baseball} + {basketball} + {soccer} we count students who play exactly 3 ports (blue section) thrice (as it is the portion of all three groups), so to count this group only once we are subtracting 2*{exactly 3 sports}.


Hope it helps.


Why it is necessary to subtract the 3 twice?

Kudos [?]: 0 [0], given: 13

Re: There are 150 students at Seward High School. 66 students   [#permalink] 11 Aug 2017, 18:28
Display posts from previous: Sort by

There are 150 students at Seward High School. 66 students

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.