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20 Sep 2019, 23:27
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jamifahad
Given:
1. A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car.
2. 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.
Asked: 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?
Please find solution in image.
IMO D
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07 Mar 2024, 01:04
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jamifahad
Given: 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.
Asked: 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?
Screenshot 2024-03-07 at 1.25.44 PM.png [ 45.63 KiB | Viewed 647 times ]
The number of people who could do all these things = 6
The number of people who could do exactly 2 of these things = 37 - 6= 31
A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car.
6 + 31 + A + B + C + D = 144
A + B + C + D = 144 - 37 = 107 --------- (1)
X + Y + Z = 31 --------------(2)
The number of people who could not swim was 89
B + C + Z + D = 89 ---------------(3)
The number of people who could not dance was 100
A + C + Y + D = 100 ----------------(4)
The number of people who could not drive a car was 91
A + B + X + D = 91 ----------------(5)
Adding (3) + (4) + (5)
2(A+B+C) + (X+Y+Z) + 3D = 89 + 100 + 91 = 280
2(107-D) + 31 + 3D = 280
214 + 31 + D = 280
D = 35
IMO D
Given: 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.
Asked: 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?
Attachment:
Screenshot 2024-03-07 at 1.25.44 PM.png [ 45.63 KiB | Viewed 647 times ]
The number of people who could do all these things = 6
The number of people who could do exactly 2 of these things = 37 - 6= 31
A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car.
6 + 31 + A + B + C + D = 144
A + B + C + D = 144 - 37 = 107 --------- (1)
X + Y + Z = 31 --------------(2)
The number of people who could not swim was 89
B + C + Z + D = 89 ---------------(3)
The number of people who could not dance was 100
A + C + Y + D = 100 ----------------(4)
The number of people who could not drive a car was 91
A + B + X + D = 91 ----------------(5)
Adding (3) + (4) + (5)
2(A+B+C) + (X+Y+Z) + 3D = 89 + 100 + 91 = 280
2(107-D) + 31 + 3D = 280
214 + 31 + D = 280
D = 35
IMO D
07 Mar 2024, 01:11
Kudos
Bookmarks
Given: 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.
Asked: 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?
Total number of people = 144
The number of people who could swim = 144 - 89 = 55
The number of people who could dance = 144 - 100 = 44
The number of people who could drive a car = 144 - 91 = 53
The number of people who could all things = 6
The number of people who could do exactly 2 things = 37 - 6 = 31
All = C1 + C2 + C3 - (exactly 2) - 2(all 3) + none
144 = 55 + 44 + 53 - 31 - 2*6 + none
none = 144 - 55 - 44 - 53 + 31 + 12 = 35
The number of people could not do any of these things = 35
IMO D
Asked: 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?
Total number of people = 144
The number of people who could swim = 144 - 89 = 55
The number of people who could dance = 144 - 100 = 44
The number of people who could drive a car = 144 - 91 = 53
The number of people who could all things = 6
The number of people who could do exactly 2 things = 37 - 6 = 31
All = C1 + C2 + C3 - (exactly 2) - 2(all 3) + none
144 = 55 + 44 + 53 - 31 - 2*6 + none
none = 144 - 55 - 44 - 53 + 31 + 12 = 35
The number of people could not do any of these things = 35
IMO D
