It is currently 26 Jun 2017, 07:20

### 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

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

### Hide Tags

CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: PS: high school sports [#permalink]

### Show Tags

16 Jun 2008, 21:46
66+45+42-27-6+x=150 ---> x=30

This equation is constructed by following principle: How we can come from (66+45+42) to 150.

1. we have to subtract 27 as we count it twice in (66+45+42)
2. we have to subtract 2*3 as we count it three times in (66+45+42)
3. we have to add x (none) as we do not count it in (66+45+42)
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Manager
Joined: 11 Sep 2009
Posts: 100
Re: PS: high school sports [#permalink]

### Show Tags

24 Oct 2009, 23:22
30 too

150 - x = 150 - [66 + 45 + 42 - N2 - 2(3)]

PS: N2 is subtracted only once because any two pairs are counted exactly twice.
N3 is subtracted twice because all three are counted exactly three times.
Intern
Joined: 14 Oct 2011
Posts: 4
Re: 150 students at seward high school. 66 play baseball, 45 [#permalink]

### Show Tags

13 Nov 2011, 11:04
These are the two formulas required in this ques:

1. Three sets A, B, and C, then
P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)

2. Number of people in exactly two of the sets =
P(AnB) + P(AnC) + P(BnC) – 3P(AnBnC)

Using 2,
27 = P(AnB) + P(AnC) + P(BnC) - 3 (3)

Hence, P(AnB) + P(AnC) + P(BnC) = 36

Put this in 1
P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)
or
P(AuBuC) = P(A) + P(B) + P(C) – [P(AnB) + P(AnC) + P(BnC)] + P(AnBnC)
=> P(AuBuC) = 66 + 42 + 45 - 36 + 3 = 120

Hence, NONE of sports is
Total - P(AuBuC) = 150-120 = 30

C is the Answer
Re: 150 students at seward high school. 66 play baseball, 45   [#permalink] 13 Nov 2011, 11:04

Go to page   Previous    1   2   [ 23 posts ]

Similar topics Replies Last post
Similar
Topics:
A school has a total enrollment of 150 students. There are 63 students 4 29 May 2017, 04:19
2 At a certain school, 40 percent of the students play rugby 2 21 Sep 2016, 12:28
A baseball team won 45 percent of the first 80 games it played. How ma 6 24 Jun 2017, 08:20
2 There are 150 students at Seward High School. 66 students 6 12 May 2017, 08:57
2 At a certain school, each of the 150 students takes between 3 07 Mar 2016, 22:50
Display posts from previous: Sort by

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

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.