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A survey was conducted to find out how many people in a housing colony
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20 Nov 2021, 01:03
20 Nov 2021, 01:03
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Question Stats:
27% (04:09) correct
72% (02:47) wrong based on 11 sessions
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A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 89, the number of people who could not dance was 100 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things?
A) 17
B) 23
C) 29
D) 35
E) 50
A) 17
B) 23
C) 29
D) 35
E) 50
Re: A survey was conducted to find out how many people in a housing colony
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22 Nov 2021, 11:16
22 Nov 2021, 11:16
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T=n(A)+n(B)+n(C)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)
T=144
n(A)=T-n(A')=144-89=55
n(B)=T-n(B')=144-100=44
n(C)=T-n(C')=144-91=53
n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6=31
n(All 3 Events)=6
144=55+44+53-31-2*6+n(None of the events)
n(None of the events)=144-55-44-53+31+12=35
Ans: "D"
T=144
n(A)=T-n(A')=144-89=55
n(B)=T-n(B')=144-100=44
n(C)=T-n(C')=144-91=53
n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6=31
n(All 3 Events)=6
144=55+44+53-31-2*6+n(None of the events)
n(None of the events)=144-55-44-53+31+12=35
Ans: "D"
Re: A survey was conducted to find out how many people in a housing colony
[#permalink]
03 May 2022, 06:34
03 May 2022, 06:34
Is this a formula to remember? Because I've never come across Venn formula when none of the events is included
Carcass wrote:
T=n(A)+n(B)+n(C)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)
T=144
n(A)=T-n(A')=144-89=55
n(B)=T-n(B')=144-100=44
n(C)=T-n(C')=144-91=53
n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6=31
n(All 3 Events)=6
144=55+44+53-31-2*6+n(None of the events)
n(None of the events)=144-55-44-53+31+12=35
Ans: "D"
T=144
n(A)=T-n(A')=144-89=55
n(B)=T-n(B')=144-100=44
n(C)=T-n(C')=144-91=53
n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6=31
n(All 3 Events)=6
144=55+44+53-31-2*6+n(None of the events)
n(None of the events)=144-55-44-53+31+12=35
Ans: "D"
