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A survey was conducted to find out how many people in a hous [#permalink]
 19 Sep 2011, 10:00
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Question Stats:
52% (03:57) correct
47% (02:31) wrong based on 2 sessions
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
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people who could swim =55
People who clould dance =44
people who could drive = 53
total number of driving,swiming and dancing events = 55 +44 +53= 152
6 people have been triple counted for their expertise, same people extra counted 12 times.
(37 - 6) = 31 people have been double counted for their expertise.
total number of different people who could do these different activities = 152 -(12 +31) =109
so people who could do nothing 144 -109 = 35
Answer D
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people who could swim =55
People who clould dance =44
people who could drive = 53
total number of driving,swiming and dancing events = 55 +44 +53= 152
6 people have been triple counted for their expertise, same people extra counted 12 times.
(37 - 6) = 31 people have been double counted for their expertise.
total number of different people who could do these different activities = 152 -(12 +31) =109
so people who could do nothing 144 -109 = 35
Answer D
please could you elaborate as to how did you get the individual nos
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How can we do this Q using the formula....
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Math Forum Moderator
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gsd85 wrote: How can we do this Q using the formula.... 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"
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Took me 5 minutes to solve. I had no idea there was such a formula. Thanks fluke.
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D.
Same logic as Fluke!
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I used to take more time to solve this type of question. Fluke's method is awesome and will help to reduce the time to solve. Thanks Fluke!!!!!!!!
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chawlavinu wrote: I used to take more time to solve this type of question. Fluke's method is awesome and will help to reduce the time to solve.
Thanks Fluke!!!!!!!! You're welcome!!! The appreciation goes to the contributors of this thread: formulae-for-3-overlapping-sets-69014.htmlesp. formulae-for-3-overlapping-sets-69014.html#p729340
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#not swim = 89 => #swim = 144-89 = 55
#not dance = 100 => #dance = 144 - 100 = 44
#not drive = 91 => #drive = 144 - 91 = 53
at least two = sum of two's + sum of three's = 37
sum of three's = 6
=> sum of two's = 31
total = S + D + Dr - (sum of two's ) - 2*(sum of three's) + none
144 = 55 + 44 + 53 -31 - 2*6 + none
=> none = 35
Answer is D.
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+1 for D.
Use 3 set formula:
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
Found individual numbers as explained in the earlier posts.
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Hey liftoff,
I used to be confused with such kind of problems and what helped me is drawing Venn. If you follow this there is no need to remember any formula. One just need ot remember simple +/- and also take less than 2 min.
Cheers
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jamifahad wrote: 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 I am not sure that stated official answer is correct one. or I am tricked by the language (which generally is the case in these kind of question). IMHO, the number of people who could do at least two of the things also includes 18 ( 3 *6 where 6 are the number of people who could all these things). My answer is coming as option B - 23. Can anybody help.
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saxenaashi wrote: jamifahad wrote: 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 I am not sure that stated official answer is correct one. or I am tricked by the language (which generally is the case in these kind of question). IMHO, the number of people who could do at least two of the things also includes 18 ( 3 *6 where 6 are the number of people who could all these things). My answer is coming as option B - 23. Can anybody help. The number of people who can do at least two things includes 6 (number of people who can do all three), not 6*3. Understand here that 37 is the number of people, not the number of instances. Hence 6 is not counted 3 times in 37. Out of 37 people, 18 people cannot do all three. Only 6 can do all three. So 31 can do exactly 2 things. I have discussed this concept in my blog post given below: http://www.veritasprep.com/blog/2012/09 ... ping-sets/Question 1 on the diagram is this.
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