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

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Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post Updated on: 27 Jan 2018, 18:45
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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

Originally posted by OCDianaOC on 27 Jan 2018, 17:45.
Last edited by chetan2u on 27 Jan 2018, 18:45, edited 1 time in total.
shifted the topic and added OA
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Re: Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 27 Jan 2018, 18:44
OCDianaOC wrote:
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


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
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Re: Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 27 Jan 2018, 18:56
chetan2u wrote:
OCDianaOC wrote:
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


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



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...
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Re: Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 27 Jan 2018, 20:07
OCDianaOC wrote:
chetan2u wrote:
OCDianaOC wrote:
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


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



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...


Hi OCDianaOC

Refer to below overlapping set diagram.

Attachment:
Venn diag.jpg
Venn diag.jpg [ 27.14 KiB | Viewed 860 times ]


As it is given that only franco or only England is 80

=>60-x+90-x=80

=>x=35
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Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 27 Jan 2018, 20:39
Thanks for sharing your venn diagram. However, I'm used to this type of overlapping sets. What am I missing here? Please help. Thanks!
Attachments

15171106654881232922396.jpg
15171106654881232922396.jpg [ 2.63 MiB | Viewed 797 times ]

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Re: Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 27 Jan 2018, 21:29
OCDianaOC wrote:
Thanks for sharing your venn diagram. However, I'm used to this type of overlapping sets. What am I missing here? Please help. Thanks!


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
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Re: Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 27 Jan 2018, 23:23
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OCDianaOC wrote:
Thanks for sharing your venn diagram. However, I'm used to this type of overlapping sets. What am I missing here? Please help. Thanks!


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

Attachment:
2 by 2 matrix.jpg
2 by 2 matrix.jpg [ 30 KiB | Viewed 713 times ]
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Re: Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 28 Jan 2018, 00:14
OCDianaOC wrote:
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


19. Overlapping Sets



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Re: Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 02 Feb 2018, 03:30
60=B'+both
90=A'+ both
150=80+ 2 both
Both =35

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Re: Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 02 Feb 2018, 03:49
Solving it by equation is not needed. Simple Sets--Overlapping will give the answer in a much easier way.
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Re: Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 05 Feb 2018, 10:19
OCDianaOC wrote:
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


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
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Of the 130 passengers on the airplace, 60 had visited France, [#permalink]

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New post 15 Feb 2018, 21:46
OCDianaOC wrote:
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



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
Of the 130 passengers on the airplace, 60 had visited France,   [#permalink] 15 Feb 2018, 21:46
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