Of the 130 passengers on the airplace, 60 had visited France,

Question

Of the 130 passengers on the airplane, 60 had visited France, 90 had visited England, and 80 had visited Franco or England, but not both. How many people had visited both Franco and England?

1) 0
2) 15
C) 25
D) 35
E) 55

chetan2u · Answer

So let F visited France alone, E visited England alone and b visited both..
So F+E+b*2=60+90……80+b*2=150……2b=70……b=35 and none=130-80-35=15
D

OCDianaOC · Answer

Thank you! How do you solve this using an overlapping sets matrix? I was able to get all the info down on mine, but fail to complete it since I now have to assign variables to complete the rest...

niks18 · Answer

Hi OCDianaOC Refer to below overlapping set diagram. Venn diag.jpg As it is given that only franco or only England is 80 =>60-x+90-x=80 =>x=35

OCDianaOC · Answer

Thanks for sharing your venn diagram. However, I'm used to this type of overlapping sets. What am I missing here? Please help. Thanks!

niks18 · Answer

Hi  OCDianaOC

the 2 by 2 matrix presented is ambiguous.

if you check the first row it can be interpreted as England & #France (which i am assuming is only France)=90-x, which is illogical and similarly for the second row.

if the common region between England and France is x, then #France will be 60-x and #England =90-x

you simply need to add these two values and get the value of x i.e. 60-x+90-x=80

niks18 · Answer

Hi OCDianaOC Responding to your PM, if you want to use the 2 by 2 matrix then it will be as mentioned below. Note there will be no common value between Only France and Only England, hence the matrix should mention value as 0. Hope this clarifies your doubt 2 by 2 matrix.jpg

Bunuel · Answer

19. Overlapping Sets 
     Theory   
 Overlapping Sets Made Easy! 
 How to draw a Venn Diagram for problems 
 ADVANCED OVERLAPPING SETS PROBLEMS  
 Formulae for 3 overlapping sets 
     Questions   
 The E-GMAT Sets Triad: 3 Exciting Sets Questions! 
 The Word “Or” in GMAT Math 
 DS Questions 
 PS Questions

For more:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

ketkichaudhary1992 · Answer

60=B'+both
90=A'+ both
150=80+ 2 both
Both =35

Sent from my   using  GMAT Club Forum mobile app

HannibalLecter · Answer

Solving it by equation is not needed. Simple Sets--Overlapping will give the answer in a much easier way.

ScottTargetTestPrep · Answer

We can create the equation:

France or England but not both = 60 - both + 90 - both

80 = 60 + 90 - 2(both)

70 = 2(both)

35 = both

Answer: D

aadarshg11 · Answer

Formula : Exactly one = F + E - 2*(both F&E)

F = 60
E = 90
Given , Exactly 1 ( either England or France) = 80

==> 80 = 60+90-2(x) ==> x=35
ie, Both F&E = x = 35.

Ans D

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Of the 130 passengers on the airplace, 60 had visited France,

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