BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Venn Diagram?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 39
Joined: Tue Jul 05, 2011 1:13 am

Venn Diagram?

by StoneBlack » Tue Jul 05, 2011 2:21 am
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

Do we get B as the OA?
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 150
Joined: Tue Mar 08, 2011 4:38 am
Thanked: 5 times

by finance » Tue Jul 05, 2011 2:42 am
it's C.

Let the number of students who play both baseball and soccer be a.
basketball and baseball be b.
basketball and soccer be c.
a+b+c= 27

We can express the number of students who play as:

66+(45-3)-b-c+(42-3)-a-c+c= 66+42+39-b-c-a=147-(a+b+c)
whic equals 147-27=120

so 120 students play, therefore 150-120=30 students play none of the games.
Top
Senior | Next Rank: 100 Posts
Posts: 39
Joined: Tue Jul 05, 2011 1:13 am

by StoneBlack » Tue Jul 05, 2011 3:21 am
Yes. Agree. Answer is C. 30 players.
Top
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Sun Jun 05, 2011 10:39 pm
Thanked: 2 times
Followed by:1 members

by worldpeace93 » Tue Jul 05, 2011 4:15 am
answer is C.
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Tue Dec 19, 2017 7:17 am
StoneBlack 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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1