Question
In a class of 120 students numbered 1 to 120, there are 3 extracurricular activities to choose from. All even numbered students opt for Dance, whose numbers are divisible by 5 opt for Music and those whose numbers are divisible by 7 opt for Debate. How many opt for none of the three subjects?
Answer: Option B
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B
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B
option (b)
A is the set of those who opted for Dance = 1202=60 students.
B is the set of those who opted for Music = 1205=24.
C is the set of those who opted for Debate = 1207=17.
The 10th, 20th, 30th…… numbered students would have opted for both Dance and Music. 12010=12.
The 14th, 28th, 42nd…. Numbered students would have opted for Dance and Debate.= 12014=8.
The 35th, 70th …. Numbered students would have opted for Music and Debate = 12035=3.
And the 70th numbered student would have opted for all three subjects.
S=101, II+3III = 23
III= 1, S-X= 20+2
101-22 = X
X=79
Therefore, number of students who did not opt for any of the three activities = 41
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