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In a recent study, 90 people were surveyed about what type of animal

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In a recent study, 90 people were surveyed about what type of animal  [#permalink]

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New post 03 Jul 2018, 09:27
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A
B
C
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E

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  45% (medium)

Question Stats:

53% (01:29) correct 47% (02:01) wrong based on 32 sessions

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In a recent study, 90 people were surveyed about what type of animal they owned as a pet. Everyone surveyed owned at least one animal. The results are shown in the Venn diagram. What percent of the respondents said they had a dog and a cat but no birds?


A. 15%
B. 17%
C. 30%
D. 46%
E. 90%

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Re: In a recent study, 90 people were surveyed about what type of animal  [#permalink]

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New post 03 Jul 2018, 13:13
Bunuel wrote:
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In a recent study, 90 people were surveyed about what type of animal they owned as a pet. Everyone surveyed owned at least one animal. The results are shown in the Venn diagram. What percent of the respondents said they had a dog and a cat but no birds?


A. 15%
B. 17%
C. 30%
D. 46%
E. 90%

Attachment:
set217.jpg


Number having both dog and cat and not birds is given by GREEN portion and sum of all portions is 90..
29+4+2+17+9+14+G=90....G=90-75=15
%=100*15/90=50/3=~17%

B
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In a recent study, 90 people were surveyed about what type of animal  [#permalink]

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New post 03 Jul 2018, 13:14
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From the question stem, we can deduce that P(Total) = 90 and P(Neither) = 0
Given data:
P(Only Dogs) = 29 | P(Only Cats) = 17 | P(Only Birds) = 14 | P(All 3) = 2 | P(Birds U Cats) = 9 | P(Birds U Dogs) = 4

Let's assume P(Dogs U Cats) to be x

P(Total) = P(Only Dogs) + P(Only Cats) + P(Only Birds) + P(Birds U Cats) + P(Birds U Dogs) + P(Dogs U Cats) + P(Neither)

Substituting the values given, we get \(90 = 29 + 17 + 14 + 9 + 4 + x + 2\)-> \(x = 90 - 75 = 15\)

Therefore, the percentage of the respondents who had a dog and a cat but no birds is \(\frac{15}{90}*100 = \frac{50}{3}\) = approximately 17%(Option B)
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In a recent study, 90 people were surveyed about what type of animal &nbs [#permalink] 03 Jul 2018, 13:14
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