150 students at seward high school. 66 play baseball, 45 : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 07:48

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 150 students at seward high school. 66 play baseball, 45

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 21 Jun 2006
Posts: 285
Followers: 1

Kudos [?]: 112 [0], given: 0

150 students at seward high school. 66 play baseball, 45 [#permalink]

### Show Tags

24 Jul 2007, 20:36
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (00:03) wrong based on 3 sessions

### HideShow timer Statistics

150 students at seward high school. 66 play baseball, 45 basketball and 42 soccer. 27 play exactly 2 sports and 3 play all 3 sports. How many of the 150 play none of the 3 sports?
Director
Joined: 09 Aug 2006
Posts: 763
Followers: 1

Kudos [?]: 192 [0], given: 0

Re: PS: high school sports [#permalink]

### Show Tags

25 Jul 2007, 00:15
ArvGMAT wrote:
150 students at seward high school. 66 play baseball, 45 basketball and 42 soccer. 27 play exactly 2 sports and 3 play all 3 sports. How many of the 150 play none of the 3 sports?

I'm getting 57 by using venn diagram method.
Senior Manager
Joined: 28 Jun 2007
Posts: 462
Followers: 3

Kudos [?]: 8 [0], given: 0

### Show Tags

25 Jul 2007, 02:23
66 + 45 + 42 - 2*27 - 3*3 = 153 - 60 = 93 play atleast one.

Ans : 57.
Current Student
Joined: 28 Dec 2004
Posts: 3384
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 282 [0], given: 2

### Show Tags

25 Jul 2007, 10:35
I get 21 ...

65+45+42-27+3=129

150-129=21 dont play anything
Senior Manager
Joined: 03 Jun 2007
Posts: 384
Followers: 3

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

### Show Tags

25 Jul 2007, 10:44
fresinha12 wrote:
I get 21 ...

65+45+42-27+3=129

150-129=21 dont play anything

I agree with the method and the answer. I made a calculation error. it has to be 21
Intern
Joined: 05 Apr 2007
Posts: 16
Followers: 0

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

### Show Tags

25 Jul 2007, 10:47
Hi fresinha12

Why have you added the triple? I think you should minus two times tripple. What do you think?
In the condition we have:
"27 play exactly 2 sports and 3 play all 3 sports"
I think that in 27 we don't have triple.
Current Student
Joined: 18 Jun 2007
Posts: 408
Location: Atlanta, GA
Schools: Emory class of 2010
Followers: 11

Kudos [?]: 40 [0], given: 0

### Show Tags

25 Jul 2007, 11:08
66 + 45 + 42 - 2*27 - 3*3 = 153 - 60 = 93 play atleast one.

Ans : 57.

I agree with this rationale, but I get 60.

66+45+42=153

2*27+3*3=63

153-63=90 that play one sport.

Therefore 150-90 = 60 that play no sport.
Senior Manager
Joined: 28 Jun 2007
Posts: 462
Followers: 3

Kudos [?]: 8 [0], given: 0

### Show Tags

25 Jul 2007, 14:40
emoryhopeful wrote:
66 + 45 + 42 - 2*27 - 3*3 = 153 - 60 = 93 play atleast one.

Ans : 57.

I agree with this rationale, but I get 60.

66+45+42=153

2*27+3*3=63

153-63=90 that play one sport.

Therefore 150-90 = 60 that play no sport.

That was a stupid one. I guess I got influenced by the previous post. Yeah... 60 looks correct.
Senior Manager
Joined: 17 Jul 2007
Posts: 288
Location: The 408
Followers: 3

Kudos [?]: 4 [0], given: 0

### Show Tags

25 Jul 2007, 15:19
23 play no sports at all.

each of the given sports have a total of 10 players that play that and at least one other sport. these add up to 127 sports participants.

150 - 127 = 23 play nothing.
Manager
Joined: 27 May 2007
Posts: 128
Followers: 1

Kudos [?]: 10 [0], given: 0

Re: PS: high school sports [#permalink]

### Show Tags

25 Jul 2007, 17:34
ArvGMAT wrote:
150 students at seward high school. 66 play baseball, 45 basketball and 42 soccer. 27 play exactly 2 sports and 3 play all 3 sports. How many of the 150 play none of the 3 sports?

Using a Venn diagram, there are 3 areas that overlap 2 sports, and 1 area that overlaps all three sports. Put 9 into each of the "double" areas (for the 27 that play 2 sports), and 3 into the center of the diagram. (Assuming that the 27 are equally divided among the sports, but that really doesn't matter). Then you can see that for each sport, you need to subtract 21. That means that, of the students that only play one sport, you have 45 in baseball, 24 in basketball, and 21 in soccer. That, plus the 27 (2 sports) and 3(3 sports)= 120 students that play sports. So 30 don't.
Senior Manager
Joined: 28 Jun 2007
Posts: 462
Followers: 3

Kudos [?]: 8 [0], given: 0

Re: PS: high school sports [#permalink]

### Show Tags

25 Jul 2007, 20:16
Robin in NC wrote:
ArvGMAT wrote:
150 students at seward high school. 66 play baseball, 45 basketball and 42 soccer. 27 play exactly 2 sports and 3 play all 3 sports. How many of the 150 play none of the 3 sports?

Using a Venn diagram, there are 3 areas that overlap 2 sports, and 1 area that overlaps all three sports. Put 9 into each of the "double" areas (for the 27 that play 2 sports), and 3 into the center of the diagram. (Assuming that the 27 are equally divided among the sports, but that really doesn't matter). Then you can see that for each sport, you need to subtract 21. That means that, of the students that only play one sport, you have 45 in baseball, 24 in basketball, and 21 in soccer. That, plus the 27 (2 sports) and 3(3 sports)= 120 students that play sports. So 30 don't.

OMG. This looks correct too. I think the number I found in the first post is actually the no. of people who play just one sport. I should have added the rest too.

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5062
Location: Singapore
Followers: 30

Kudos [?]: 356 [0], given: 0

### Show Tags

25 Jul 2007, 20:55
Set up a venn diagram with the following:
#(all three) = 3
#(soccer and baseball) = z

So x+y+z = 27

#(none) = n

63-x-z + 42-x-y + 39-y-z + x + y + z + 3 + n= 150
147-x-y-z+n= 150
147 - (x+y+z) + n = 150
147 - (27) + n = 150
n = 30

Sorry, too tired and lazy to draw it out =(
Director
Joined: 09 Aug 2006
Posts: 763
Followers: 1

Kudos [?]: 192 [0], given: 0

### Show Tags

26 Jul 2007, 00:11
ywilfred wrote:
Set up a venn diagram with the following:
#(all three) = 3
#(soccer and baseball) = z

So x+y+z = 27

#(none) = n

63-x-z + 42-x-y + 39-y-z + x + y + z + 3 + n= 150
147-x-y-z+n= 150
147 - (x+y+z) + n = 150
147 - (27) + n = 150
n = 30

Sorry, too tired and lazy to draw it out =(

Great explanation. Thanks a lot. Helped me correct my mistake with the venn diagram.

Using the formula for 3 overlapping sets we get 30 as well.
Senior Manager
Joined: 17 Jul 2007
Posts: 288
Location: The 408
Followers: 3

Kudos [?]: 4 [0], given: 0

Re: PS: high school sports [#permalink]

### Show Tags

26 Jul 2007, 15:09
Robin in NC wrote:
ArvGMAT wrote:
150 students at seward high school. 66 play baseball, 45 basketball and 42 soccer. 27 play exactly 2 sports and 3 play all 3 sports. How many of the 150 play none of the 3 sports?

Using a Venn diagram, there are 3 areas that overlap 2 sports, and 1 area that overlaps all three sports. Put 9 into each of the "double" areas (for the 27 that play 2 sports), and 3 into the center of the diagram. (Assuming that the 27 are equally divided among the sports, but that really doesn't matter). Then you can see that for each sport, you need to subtract 21. That means that, of the students that only play one sport, you have 45 in baseball, 24 in basketball, and 21 in soccer. That, plus the 27 (2 sports) and 3(3 sports)= 120 students that play sports. So 30 don't.

duh. what a dumb mistake I made. great write-up.
Current Student
Joined: 28 Dec 2004
Posts: 3384
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 282 [0], given: 2

### Show Tags

27 Jul 2007, 12:19
you minus the doubles cause you have counted them twice, once when we are given the number of basket ball player, football etc..you add the triple cause triple +single -double will give you the total number of players...

try it with a simple example..

Andrey2010 wrote:
Hi fresinha12

Why have you added the triple? I think you should minus two times tripple. What do you think?
In the condition we have:
"27 play exactly 2 sports and 3 play all 3 sports"
I think that in 27 we don't have triple.
Director
Joined: 26 Feb 2006
Posts: 904
Followers: 4

Kudos [?]: 107 [0], given: 0

### Show Tags

27 Jul 2007, 12:27
ywilfred wrote:
Set up a venn diagram with the following:
#(all three) = 3
#(soccer and baseball) = z

So x+y+z = 27

#(none) = n

63-x-z + 42-x-y + 39-y-z + x + y + z + 3 + n= 150
147-x-y-z+n= 150
147 - (x+y+z) + n = 150
147 - (27) + n = 150
n = 30

Sorry, too tired and lazy to draw it out =(

nothing to add. but i do differently

total = x + y + z - (xy + yz + xz) - 2(xyz) + n
150 = 66 + 45 + 42 - (27) - 2(3) + n
n = 30
Intern
Joined: 20 Jul 2007
Posts: 13
Followers: 0

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

### Show Tags

31 Jul 2007, 02:12
Himalayan wrote:
ywilfred wrote:
Set up a venn diagram with the following:
#(all three) = 3
#(soccer and baseball) = z

So x+y+z = 27

#(none) = n

63-x-z + 42-x-y + 39-y-z + x + y + z + 3 + n= 150
147-x-y-z+n= 150
147 - (x+y+z) + n = 150
147 - (27) + n = 150
n = 30

Sorry, too tired and lazy to draw it out =(

nothing to add. but i do differently

total = x + y + z - (xy + yz + xz) - 2(xyz) + n
150 = 66 + 45 + 42 - (27) - 2(3) + n
n = 30

Hi Himalayan,

However, could you plz tell me if it is the standard formula which you have used to solve the problem.

Regards

Nikhil
Current Student
Joined: 28 Dec 2004
Posts: 3384
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 282 [0], given: 2

### Show Tags

02 Aug 2007, 09:14
I am still sticking with 21.....

whats the OA??
Manager
Joined: 14 May 2007
Posts: 178
Location: India
Followers: 2

Kudos [?]: 70 [0], given: 11

### Show Tags

16 Jun 2008, 04:35
[quote="ywilfred"]Set up a venn diagram with the following:
#(all three) = 3
#(soccer and baseball) = z

So x+y+z = 27

#(none) = n

63-x-z + 42-x-y + 39-y-z + x + y + z + 3 + n= 150
147-x-y-z+n= 150
147 - (x+y+z) + n = 150
147 - (27) + n = 150
n = 30

Sorry, too tired and lazy to draw it out =([/quote]

Great explanation, was stuck in this ques for a while. Thanks.
Manager
Joined: 11 Apr 2008
Posts: 128
Location: Chicago
Followers: 1

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

### Show Tags

16 Jun 2008, 13:02
ioiio wrote:
66 + 45 + 42 - 2*27 - 3*3 = 153 - 60 = 93 play atleast one.

Ans : 57.

ioiio, you are correct except you don't multiply the 27 by 2. The 27 figure encompasses all 2-sport individuals and thus no manipulation is needed. The formula is:
A + B + C -AB - AC - BC - 2ABC + Neither = Total

In this problem, it states that AB + AC + BC = 27 --> don't need to multiply by 2.

Plus, the 3 figure is multiplied by 2, not 3.

_________________

Factorials were someone's attempt to make math look exciting!!!

Re:   [#permalink] 16 Jun 2008, 13:02

Go to page    1   2    Next  [ 23 posts ]

Similar topics Replies Last post
Similar
Topics:
2 At a certain school, 40 percent of the students play rugby 2 20 Sep 2016, 12:49
A baseball team won 45 percent of the first 80 games it played. How ma 3 20 Dec 2015, 05:11
1 There are 150 students at Seward High School. 66 students 5 14 Dec 2010, 06:23
2 At a certain school, each of the 150 students takes between 3 25 Jul 2010, 11:37
13 All of the students of Music High School are in the band, 8 24 Aug 2008, 21:15
Display posts from previous: Sort by