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If 45% of study participants liked dogs, 60% liked cats, and 25% liked

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Senior Manager
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Concentration: General Management, Operations
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If 45% of study participants liked dogs, 60% liked cats, and 25% liked  [#permalink]

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New post 12 Sep 2015, 12:29
1
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (00:57) correct 22% (01:10) wrong based on 71 sessions

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If 45% of study participants liked dogs, 60% liked cats, and 25% liked neither, what percent liked both cats and dogs?

A. 15%
B. 20%
C. 25%
D. 30%
E. 35%

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Re: If 45% of study participants liked dogs, 60% liked cats, and 25% liked  [#permalink]

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New post 12 Sep 2015, 21:57
1
In overlappping sets

Total-N=A+B -both.

N=neither,

A=Number of people in category A and both groups

B=Number of people in category B and both gorups

Both=number of people in both groups,

25% liked neither so total-n=75%=60%+45%-both
=30%.
so option D is correct
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If 45% of study participants liked dogs, 60% liked cats, and 25% liked  [#permalink]

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New post 27 Jan 2019, 01:41
shasadou wrote:
If 45% of study participants liked dogs, 60% liked cats, and 25% liked neither, what percent liked both cats and dogs?

A. 15%
B. 20%
C. 25%
D. 30%
E. 35%


Let total number of people participated be \(= 100\)

\(45\)% of total liked dogs \(= 45\)% of \(100 = \frac{45}{100}*100 = 45\)

\(60\)% of total liked cats \(= 60\)% of \(100 = \frac{60}{100}*100 = 60\)

\(25\)% of total liked neither \(= 25\)% of \(100 = \frac{25}{100}*100 = 25\)

Total \(=\) Liked Dogs \(+\) Liked Cats \(-\) Liked Both \(+\) Liked Neither

\(100 = 45 + 60\) \(-\) Liked Both \(+ 25\)

\(100 = 130\) \(-\) Liked Both

Liked Both \(= 130 - 100 = 30\)

Therefore Percentage of people participated liked both cats and dogs \(= 30\)%

Answer D
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If 45% of study participants liked dogs, 60% liked cats, and 25% liked   [#permalink] 27 Jan 2019, 01:41
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If 45% of study participants liked dogs, 60% liked cats, and 25% liked

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