A high school has 400 students 1/2 attend the airthmetic

Question

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

A. 50
B. 75
C. 150
D. 200
E. 300

jko · Accepted Answer

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

MHIKER · Answer

A= 200, A only = 200-150 = 50
B= 250, B only = 250-150 = 100
C=300 , C only = 300- 150 = 150
Exactly two two courses = 50+100+150+150(All)-400=50 Ans.

rxs0005 · Answer

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 ?

fluke · Answer

The way you used it, the formula looks fine. Please see the following link as well:
 https://gmatclub.com/forum/overlapping-sets-problems-87628.html#p759888

AB have only doubly counted values that is unique to only A and B not C right;  right

In 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

subhashghosh · Answer

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

raghupara · Answer

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

fluke · Answer

overlapping-sets-problems-87628.html#p759888

raghupara · Answer

Very clear!
Thanks Fluke.

LalaB · Answer

(1/2)+(5/8)+(3/4)-x-2*(3/8)+0=1
x=1/8

1/8*400=50

AlyoshaKaramazov · Answer

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.

TGC · Answer

Total=A+B+C-(Exactly 2 Groups) - 2*All three

Exactly 2 Groups = X

400=200+250+300-X-2*150

X=50

Asifpirlo · Answer

Exactly two = 200+250+300-300-400 = 50 (Answer)

chandruattcs · Answer

Hi Everyone

, I have a simple formula two and three group overlaps. Total = Group 1 + Group 2 - both + neither Total = Group 1 + Group 2 + Group 3 - (Sum of two group overlaps) - 2(All three group overlaps) + neither Using the above formula, 400 = 200 + 250 +300 -Sum of all two group overlaps - 2(150) + 0 (since it is given - every student attends at least one club) So sum of two group overlaps = 50 :-D

Answer A. Thanks, Chandru

nilapriya · Answer

@Chandru yeah..its pretty easy!!!! :lol:

Thanks, Nila

Bunuel · Answer

Theory on advanced overlapping sets problems: advanced-overlapping-sets-problems-144260.html

MHIKER · Answer

A=200
B=250
C=300
ALL THREE = 150
EXACTLY TWO = X

TOTAL = A+B+C-EXACTLY 2-2(ALL THREE)
400= 200+250+300-X-2(150)
X=50

THE ANSWER IS A.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A high school has 400 students 1/2 attend the airthmetic

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A high school has 400 students 1/2 attend the airthmetic

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards