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01 Feb 2023, 12:45
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
56% (01:41) correct
44%
(01:43)
wrong
based on 252
sessions
History
Date
Time
Result
Not Attempted Yet
Each of the hundred students in a class enrolled in at least one of the three activities: Singing, Dancing, and Theatre. If 40 participated in Singing, 50 participated in Dancing and 40 participated in Theatre and if 10 participated in all the three activities, how many students participated in at least two activities?
A. 10
B. 20
C. 24
D. 30
E. 32
A. 10
B. 20
C. 24
D. 30
E. 32
yashikaaggarwal
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01 Feb 2023, 15:55
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The answer is B, you can refer to the solution in the picture in the attachment.
Posted from my mobile device
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IMG_20230201_225410.jpg [ 1020.35 KiB | Viewed 3923 times ]
02 Feb 2023, 03:26
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Bunuel
Solution:
- We can make the following venn diagram based on this diagramAttachment:
singdance.png [ 11.82 KiB | Viewed 3684 times ]
- According to the venn diagram, \(a+b+c+d+e+f+10=100\) or \(a+b+c+d+e+f=90........(i)\)
- We also know
- 40 participated in Singing i.e., \(a+d+e+10=40\) or \(a+d+e=30........(ii)\)
- 50 participated in Dancing i.e., \(b+e+f+10=50\) or \(b+e+f=40........(iii)\)
- 40 participated in Theatre i.e., \(c+d+f+10=40\) or \(c+d+f=30........(iv)\)
- We are asked the value of \(d+e+f+10\)
- Upon adding equations ii, iii and iv, we get: \((a+b+c+d+e+f)+d+e+f=30+40+30\)
\(⇒90+d+e+f=100\)
\(⇒d+e+f=10\)
\(⇒d+e+f+10=20\)
Hence the right answer is Option B
