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

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Senior Manager
Joined: 12 Aug 2015
Posts: 280
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
If 45% of study participants liked dogs, 60% liked cats, and 25% liked  [#permalink]

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12 Sep 2015, 12:29
1
1
00:00

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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Manager
Status: single
Joined: 19 Jan 2015
Posts: 84
Location: India
GPA: 3.2
WE: Sales (Pharmaceuticals and Biotech)
Re: If 45% of study participants liked dogs, 60% liked cats, and 25% liked  [#permalink]

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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
Director
Joined: 04 Dec 2015
Posts: 743
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
If 45% of study participants liked dogs, 60% liked cats, and 25% liked  [#permalink]

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27 Jan 2019, 01:41
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 $$= 30$$%

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