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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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A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

68% (00:47) correct
32% (01:13) wrong based on 466 sessions

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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?

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

So, answer will be B Hope it helps!
_________________

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?

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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\(@apoorvarora\)

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?

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.

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

We can use the following formula:

total pet owners = # who own dogs + # who own cats + # who own rabbits - # who own exactly two types - 2 x # who own three types + # who own none

Thus:

60 = 40 + 30 + 10 - 12 - 2T + 0

60 = 68 - 2T

2T = 8

T = 4

Answer: B
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

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03 Sep 2017, 21:05

Hi Bunuel, This is my first post after learning and watching solutions by all experts. I solved this and got the right answer, however I approached it in a different way but was quicker for me to understand. Please advise if this is also an alternate way? Total 60. Exactly 2 pets : CD,CR,DR = 12. As we are asked to find common among total 3 group : I just divided 12/3 : 4.

I know the method was ridiculous. However please advise the correct way or if this can be used?

Hi Bunuel, This is my first post after learning and watching solutions by all experts. I solved this and got the right answer, however I approached it in a different way but was quicker for me to understand. Please advise if this is also an alternate way? Total 60. Exactly 2 pets : CD,CR,DR = 12. As we are asked to find common among total 3 group : I just divided 12/3 : 4.

I know the method was ridiculous. However please advise the correct way or if this can be used?

Best regards

No, this is not correct. The number of people who owned exactly two of the three types of pet is not always thrice the number of people who owned all three.

Foe example, if the number of people who owned exactly two of the three types of pet were 18 instead of 12, the answer would be 1, not 18/3 = 6 (from Total = C + D + R - Exactly two - 2*All three + Neither).

There are several correct approaches above and here is a link which explains the theory behind the formula used: 3 overlapping sets with theory, diagrams and examples: ADVANCED OVERLAPPING SETS PROBLEMS.