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In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football?
  • a)
    4
  • b)
  • c)
    10
  • d)
    12
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a school every student is assigned a unique identification number. ...
The required number should be completely divisible by both 4 and 6. That means it should be divisible by LCM of 4 and 6, which is 12. Such 8 numbers are possible which are completely divisible by 12. They are 12, 24, 36, 48, 60, 72, 84 and 96.
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In a school every student is assigned a unique identification number. ...
Solution:

We need to find the number of students who play both cricket and football. This can be found by finding the common multiples of 4 and 6.

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96

Common multiples of 4 and 6: 12, 24, 36, 48, 60, 72, 84, 96

Out of these, only 8 numbers are between 1 and 100. Therefore, there are 8 students who play both cricket and football.

Answer: Option B (8)
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Community Answer
In a school every student is assigned a unique identification number. ...
The number would be 12,24,36,48,60,72,84,96
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