3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?
A)1/8
B)1/4
C)3/8
D)1/2
E)5/8
OAA
Clubs
This topic has expert replies
-
- Legendary Member
- Posts: 510
- Joined: Thu Aug 07, 2014 2:24 am
- Thanked: 3 times
- Followed by:5 members
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Here is the formula for 3 overlapping groups:3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?
(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 5/8
Total = Group 1 + Group 2 + Group 3 - (those in 2 of the groups) - 2(those in all 3 groups)
The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in club A, everyone in club B, and everyone in club C:
Those in exactly 2 of the clubs are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 clubs are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.
In the problem above:
Let Total = 8.
Group 1 = Albanian = (1/2)8 = 4.
Group 2 = Bardic = (5/8)8 = 5.
Group 3 = Checkmate = (3/4)8 = 6.
Those in exactly 2 clubs = x.
Those in all 3 clubs = (3/8)8 = 3.
Plugging these values into the formula, we get:
8 = 4 + 5 + 6 - x - 2(3)
x = 1.
Thus:
(Those in exactly 2 of the clubs)/total = 1/8.
The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
j_shreyans wrote:3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?
A)1/8
B)1/4
C)3/8
D)1/2
E)5/8
OAA
- Attachments
-
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7266
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can let the total number of students = 8, and thus:j_shreyans wrote:3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?
A)1/8
B)1/4
C)3/8
D)1/2
E)5/8
Since 3/8 of all students are in all 3 clubs, 3 students are in all 3 clubs
Since 1/2 of all students are in Albanian, 4 students are in Albanian
Since 5/8 of all students are in Bardic, 5 students are in Bardic
Since 3/4 of all students are in Checkmate, 6 students are in Checkmate.
From the given information, we know that 0 students are in none
Letting t = the number of students in exactly two clubs, we can now use the equation:
Total = A + B + C - (exactly two clubs) -2(all three clubs) + none
8 = 4 + 5 + 6 - t - 2(3) + 0
8 = 15 - t - 6
t = 1
So, 1/8 are in exactly two clubs.
Answer: A
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews