|
Author |
Message |
|
TAGS:
|
|
|
Director
Joined: 07 Jun 2004
Posts: 641
Location: PA
Followers: 1
Kudos [?]:
60
[0], given: 22
|
A high school has 400 students 1/2 attend the airthmetic [#permalink]
 17 Mar 2011, 15:55
Question Stats:
45% (02:18) correct
54% (02:25) wrong based on 1 sessions
A high school has 400 students 1/2 attend the airthmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 3/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs. A. 50 B. 75 C. 150 D. 200 E. 300 can you please solve this using a 3 circle venn diagram
_________________
If the Q jogged your mind do Kudos me : )
Last edited by rxs0005 on 18 Mar 2011, 04:27, edited 1 time in total.
|
|
|
|
|
|
|
Ross Thread Master
Joined: 17 Mar 2011
Posts: 455
Location: United States (DC)
Concentration: General Management, Technology
GMAT 1: 760 Q49 V45
GPA: 3.37
WE: Information Technology (Consulting)
Followers: 10
Kudos [?]:
137
[0], given: 5
|
Re: venn diagram 3 sets problem [#permalink]
18 Mar 2011, 05:50
rxs, a venn diagram is not necessary for this question, though it may help you visualize the solution.
Basically, this question is asking you to figure out how many students are being double-counted.
A-Club has 200 members (1/2 of 400)
B-Club has 250 members (5/8 of 400)
C-Club has 300 members (3/4 of 400)
If you add these numbers up, you can see that the three clubs combined have 750 students.
The difference between 750 and 400 is due to students being double or triple counted because they are in more than one club.
We can create an equation to solve this:
200+250+300 = n + x + 2y
where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.
The question provides y for us (150).
750 = 400 + x + 300
x = 50
|
|
|
|
|
|
Director
Status: GMAT Learner
Joined: 14 Jul 2010
Posts: 672
Followers: 21
Kudos [?]:
108
[0], given: 31
|
Re: venn diagram 3 sets problem [#permalink]
18 Mar 2011, 07:10
|
|
|
|
|
|
Director
Joined: 07 Jun 2004
Posts: 641
Location: PA
Followers: 1
Kudos [?]:
60
[0], given: 22
|
Re: venn diagram 3 sets problem [#permalink]
18 Mar 2011, 07:34
thanks i need some clarification on the below For the set overlap i have the below formula Total = A + B + C - AB - BC - CA - 2ABC ----------- ( 1 ) Applying this i get 400 = 200 + 250 + 300 - ( AB + BC + CA ) - 2* 150 sovling this we get AB + BC + CA = 750 - 400 - 300 = 50 My Q is the Formula ( 1) correct and does AB have only doubly counted values that is unique to only A and B not C right ?
_________________
If the Q jogged your mind do Kudos me : )
|
|
|
|
|
|
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2100
Followers: 108
Kudos [?]:
654
[0], given: 376
|
Re: venn diagram 3 sets problem [#permalink]
18 Mar 2011, 08:10
rxs0005 wrote: thanks i need some clarification on the below
For the set overlap i have the below formula
Total = A + B + C - AB - BC - CA - 2ABC ----------- ( 1 )
Applying this i get
400 = 200 + 250 + 300 - ( AB + BC + CA ) - 2* 150
sovling this we get
AB + BC + CA = 750 - 400 - 300 = 50
My Q is the Formula ( 1) correct
and does AB have only doubly counted values that is unique to only A and B not C right ? The way you used it, the formula looks fine. Please see the following link as well: http://gmatclub.com/forum/overlapping-sets-problems-87628.html#p759888AB have only doubly counted values that is unique to only A and B not C right; rightIn the above formula; Total = A + B + C - AB - BC - CA - 2ABC A = Only A + only AB + only AC + only ABC B = Only B + only AB + only BC + only ABC C = Only C + only AC + only BC + only ABC AB = Only AB, but not C BC = Only BC, but not A AC = Only AC, but not B ABC = Only ABC Total = Only A + Only B + Only C + Only AB + Only AC + Only BC + Only ABC + None
_________________
~fluke
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
SVP
Joined: 16 Nov 2010
Posts: 1719
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 26
Kudos [?]:
227
[0], given: 34
|
Re: venn diagram 3 sets problem [#permalink]
19 Mar 2011, 00:21
ABC = 150 A + AB + AC + ABC = 200 B + AB + BC + ABC = 250 C + AC + BC + ABC = 300 A + B + C + 2(AB + BC + AC) + 3ABC = 750 Also, A + B + C + AB + BC + AC + ABC = 400 => AB + BC + AC + 2ABC = 350 => AB + BC + AC = 350 - 300 = 50 Answer - A
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 16 Oct 2011
Posts: 130
Location: United States
Followers: 0
Kudos [?]:
9
[0], given: 5
|
Re: venn diagram 3 sets problem [#permalink]
30 Oct 2011, 07:48
Hi ppl,
I have a really fundamental doubt.
In some places, I see a formula
AuBuC = A + B + C - AnB -BnC - AnC + AnBnC
In others,
AuBuC = A + B + C - AnB -BnC - AnC - 2(AnBnC)
Pls clarify which is correct or when to apply what.
Thanks
|
|
|
|
|
|
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2100
Followers: 108
Kudos [?]:
654
[0], given: 376
|
Re: venn diagram 3 sets problem [#permalink]
30 Oct 2011, 07:58
raghupara wrote: Hi ppl,
I have a really fundamental doubt.
In some places, I see a formula
AuBuC = A + B + C - AnB -BnC - AnC + AnBnC
In others,
AuBuC = A + B + C - AnB -BnC - AnC - 2(AnBnC)
Pls clarify which is correct or when to apply what.
Thanks overlapping-sets-problems-87628.html#p759888
_________________
~fluke
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 16 Oct 2011
Posts: 130
Location: United States
Followers: 0
Kudos [?]:
9
[0], given: 5
|
Re: venn diagram 3 sets problem [#permalink]
01 Nov 2011, 10:08
fluke wrote: raghupara wrote: Hi ppl,
I have a really fundamental doubt.
In some places, I see a formula
AuBuC = A + B + C - AnB -BnC - AnC + AnBnC
In others,
AuBuC = A + B + C - AnB -BnC - AnC - 2(AnBnC)
Pls clarify which is correct or when to apply what.
Thanks overlapping-sets-problems-87628.html#p759888Very clear! Thanks Fluke.
|
|
|
|
|
|
Senior Manager
Joined: 23 Oct 2010
Posts: 335
Location: Azerbaijan
Followers: 6
Kudos [?]:
68
[0], given: 67
|
Re: venn diagram 3 sets problem [#permalink]
08 Mar 2012, 03:01
(1/2)+(5/8)+(3/4)-x-2*(3/8)+0=1 x=1/8 1/8*400=50
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true
|
|
|
|
|
|
Intern
Joined: 25 Jun 2012
Posts: 33
Followers: 0
Kudos [?]:
13
[0], given: 4
|
Re: A high school has 400 students 1/2 attend the airthmetic [#permalink]
10 Dec 2012, 20:26
The second formula described by Bunuel for 3 overlapping sets works here as well to find the last remaining "exactly" scenario.
Instead of the "in all three groups" value being the variable, the "in exactly 2 groups" is the variable and solve the equation the exact same way.
|
|
|
|
|
|
|
Re: A high school has 400 students 1/2 attend the airthmetic
[#permalink]
10 Dec 2012, 20:26
|
|
|
|
|
|
|
|
|
|
|
close
