Q#13: Students in a class

In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, those whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math.

Given this information, how many opt for none of the three subjects?

-From erik@interviewqs.com

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ANSWER:

This question tests your understanding of statistics, specifically set theory. Recall from set theory, A U B U C = A + B + C - (A n B + B n C + C n A) + (A n B n C) where U is union and n for intersection. For the purpose of this question:
- A = students in Physics (120 /2 = 60)
- B = students in Chemistry (120/5 = 24)
- C = students in Math (120/7 *round down* = 17)

Now to find the intersection values, use the LCM (least common multiple) between the divisors, ie 2 and 5 is 10, 5 and 7 is 35:
- A n B = 120/10 = 12
- B n C = 120/35 *round down* = 3
- C n A = 120/14 *round down* = 8

Finally find A n B n C is the same method finding LCM between all three divisors in this case it is only the number 70:
- A n B n C = 120/70 *round down*= 1

Thus A U B U C = 60 + 24 + 17 — (12+3+14) + 1 = 79

Now the question asks us to find those in none of the classes:
So, 120–79 = 41 students in no classes.