# A Class has 100 students with roll number from 101 to 200. All the even numbered students study Physics, whose roll number are divisible by 5 study Ch

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A Class has 100 students with roll number from 101 to 200. All the even numbered students study Physics, whose roll number are divisible by 5 study Chemistry & students with roll numbers divisible by 7 study Biology. How many students do not study any of the given subject Physics, Chemistry or Biology ?
1. 35
2. 45
3. 51
4. 62

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Correct Answer - Option 1 : 35

Given:

A Class has 100 students with roll number from 101 to 200

Formula used:

n(P ∪ C ∪ B) = n(P) + n(P) + n(C) + n(B) – n(P ∩ B) – n(P ∩ C) – n(C ∩ B) + n(P ∩ C ∩ B)

Calculation:

Physics students be P

Chemistry students be C

Biology students be B

⇒ (100/2) + (100/5) + (100/7) – [100/LCM(2,7)] – [100/LCM(2,5)] – [100/LCM(5,7)] + [100/LCM(2, 5, 7)]

⇒ [50 + 20 + 14.28 – (100/14) – (100/10) – (100/35) + (100/70)]

⇒ (50 + 20 + 14.28 – 7.14 – 10 – 2.85 + 1.42)

⇒ (50 + 20 + 14 – 7 – 10 – 2 + 1)

⇒ 66

Students do not study any exam = ∪ – n(P ∪ C ∪ B)

⇒ 100 – 66 = 34 in approximately 35

∴ Students do not study any exam is 35.