QUESTION

CSAT

Easy

Reasoning

Prelims 2019

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?

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Explanation

To play both sports, a student's number must be divisible by both 4 and 6.

The LCM of 4 and 6 is 12. This means any number divisible by 12 is divisible by both 4 and 6.

The multiples of 12 with this range of 1 to 100 are: 12, 24, 36, 48, 60, 72, 84, and 96. There are 8 such numbers.

Therefore, 8 students play both football and cricket.

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