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# In the city of San Durango, 60 people own cats, dogs, or rab

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In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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02 Dec 2012, 01:45
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In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?

A 2
B 4
C 8
D 12
E 32
[Reveal] Spoiler: OA
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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02 Dec 2012, 02:08
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apoorvarora wrote:
In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?

A 2
B 4
C 8
D 12
E 32

Total = C + D + R - (CD + DR + CR) - 2CDR

60 = 30 + 40 + 10 - (12) - 2x

x = 4

Hope it helps!
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Last edited by BrushMyQuant on 02 Dec 2012, 02:23, edited 1 time in total.
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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02 Dec 2012, 02:16
No the ans is 4...

You are considering a case when cat dogs and rabbit are not exactly equal to 12 .

The solution shall be 60=30+40+10-12-2x

and hence x shall be 4.
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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02 Dec 2012, 02:19
Total = C + D + R - Exactly two - 2*All three

60 = 30 + 40 + 10 - 12 - 2x

2x = 8

x = 4
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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02 Dec 2012, 02:23
apoorvarora wrote:
No the ans is 4...

You are considering a case when cat dogs and rabbit are not exactly equal to 12 .

The solution shall be 60=30+40+10-12-2x

and hence x shall be 4.

thanks.. i should hv not tried it dng in my head. updated the solution
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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02 Dec 2012, 04:12
Expert's post
apoorvarora wrote:
In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?

A 2
B 4
C 8
D 12
E 32

3 overlapping sets with theory, diagrams and examples: ADVANCED OVERLAPPING SETS PROBLEMS
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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09 Dec 2012, 00:19
Can any1 show it by using venn diagrams?
I tried to set up the equation as follows:
People owning all 3 pets = 'X'.

People owning cats and dogs only = a

Owning rabbits and cats only = b

Owning dogs and rabbits only = c

Then i set up eqn as follows to find X

30-(a+b+x) + 40-(a+x+c) +10 - (b+x+c) = 60

and got the equation:

80-2(a+b+c)-3X = 60

also,can we select either a+c =12 or b+c =12 or a + b=12?

Thanks,
Shreeraj
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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09 Dec 2012, 00:54
You can refer to link provided by bunnel...

Still if u face prob let me know...i shall post the solution
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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09 Dec 2012, 07:12
Actually i dont want to use the formulas.
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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09 Dec 2012, 10:19
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Expert's post
$$@apoorvarora$$

when a problem is like you posted here or similar, like this one

Quote:
Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?

is much better to use the formula Total = C + D + R - Exactly two - 2*All three (refers also to the post linked by Bunuel (the second one)

$$IF$$ the problem is like this

Quote:
Workers are grouped by their areas of expertise, and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers are on both the Sales and Vision teams, 9 workers are on both the Marketing and Vision teams, and 4 workers are on all three teams. How many workers are there in total?

or this

Quote:
The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedy movies are there?
(souce MGMAT)

you can use either $$venn diagram$$ or the formula $$Total= A+B+C - (AnB+AnC+BnC) +AnBnC + Neither$$ is the same thing: it depends on which you are more comfortable

In the first case, that is the case of the question of the post at stake, is much better use the formula because is faster ans because set up a Venn diagram is more convoluted and prone of errors. Try to stay flexible.

Hope this is useful
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Last edited by carcass on 09 Dec 2012, 10:30, edited 1 time in total.
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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09 Dec 2012, 10:27
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@ shreeraj

Just check u cant take any two values to be 12

i.e a+ c =12 is not possible coz we are given exact value as 12 and not either of the 2 value as 12...a+b+c-x will be 12...
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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09 Dec 2012, 12:26
1
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shreerajp99 wrote:
Actually i dont want to use the formulas.

I've tried my best to put this into Venn form.... From the below figure, we can see that

Cats + Dogs + Rabbits - Total - Exactly Two = All Three + All Three

Dividing this by 2, we get what "All Three" is.

As you can see, venn diagramming in this case is quite tedious and when the question has "Exactly Two" in it, it is better to use the formula.
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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10 Dec 2012, 00:17
The problem with Venn diagramming in this case is that we do not know in what ratio the "exactly two" is divided into each group.
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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16 Nov 2013, 08:38
MacFauz wrote:
Total = C + D + R - Exactly two - 2*All three

60 = 30 + 40 + 10 - 12 - 2x

2x = 8

x = 4

Why is the total number of "exactly two" that we are subtracting only 12?
Why is it not 36?
For each pair of groups we have one overlap... So for 3 pairs of groups,
we should have 3*12 = 36...
No?
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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16 Nov 2013, 08:44
Expert's post
ronr34 wrote:
MacFauz wrote:
Total = C + D + R - Exactly two - 2*All three

60 = 30 + 40 + 10 - 12 - 2x

2x = 8

x = 4

Why is the total number of "exactly two" that we are subtracting only 12?
Why is it not 36?
For each pair of groups we have one overlap... So for 3 pairs of groups,
we should have 3*12 = 36...
No?

Please check this: 3 overlapping sets with theory, diagrams and examples - ADVANCED OVERLAPPING SETS PROBLEMS
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In the city of San Durango, 60 people own cats, dogs, or [#permalink]

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17 Jan 2014, 07:46
In the city of San Durango, 60 people own cats, dogs, or rabbits.
If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and
12 owned exactly two of the three types of pet, how many people owned all three?

A) 2
B) 4
C) 8
D) 12
E) 32
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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18 Jan 2014, 15:38
ronr34 wrote:
MacFauz wrote:
Total = C + D + R - Exactly two - 2*All three

60 = 30 + 40 + 10 - 12 - 2x

2x = 8

x = 4

what is 2x representing...or better yet....where did you get 2x from (because every animal has now been counted twice?)
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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19 Jan 2014, 09:06
Expert's post
TroyfontaineMacon wrote:
ronr34 wrote:
MacFauz wrote:
Total = C + D + R - Exactly two - 2*All three

60 = 30 + 40 + 10 - 12 - 2x

2x = 8

x = 4

what is 2x representing...or better yet....where did you get 2x from (because every animal has now been counted twice?)

All that is explained here: ADVANCED OVERLAPPING SETS PROBLEMS.

Hope it helps.
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Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

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Re: In the city of San Durango, 60 people own cats, dogs, or rab   [#permalink] 03 Dec 2015, 16:20
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