Which topic do you like?

Probability Level 2

All 500 students of a class are assigned a natural number from 1 to 500. Those students who are assigned an even number love Mathematics. Those students who are assigned a number divisible by 3 love Chemistry. Those students who are assigned a number divisible by 4 love Physics. Then how many students love neither Maths nor Chemistry nor Physics?

The answer is 167.

1 solution

Ashish Menon
Apr 29, 2016

Number of students who love Maths = $\lfloor{\dfrac{500}{2}}\rfloor = 250$

Number of students who love Chemistry = $\lfloor{\dfrac{500}{3}}\rfloor = 166$

Number of students who love Physics = $\lfloor{\dfrac{500}{4}} = 125$

Number of students who love Maths and Chemistry = $\lfloor{\dfrac{500}{\text{L.CM of 2 and 3}}}\rfloor = 83$

Number of students who love Physics and Chemistry = $\lfloor{\dfrac{500}{\text{L.CM of 3 and 4}}}\rfloor = 41$

Number of students who love Maths and Physics = $\lfloor{\dfrac{500}{\text{L.CM of 2 and 4}}}\rfloor = 125$

Number of students who love Maths and Chemistry and Physics = $\lfloor{\dfrac{500}{\text{L.CM of 2, 3 and 4}}}\rfloor = 41$

Number of students who love Maths and Chemistry only = $83 - 41 = 42$

Number of students who love Physics and Chemistry only = $41 - 41 = 0$

Number of students who love Maths and Physics only = $125 - 41 = 84$

Number of students who love Maths only = $250 - (42 + 41 + 84) = 83$

Number of students who love Chemistry only = $166 - (42 + 41) = 83$

Number of students who love Physics only = $125 - (84 + 41) = 0$

Number of students who dont love any of the subjects = $500 - (83 + 42 + 41 + 84 + 83 + 0 + 0)\\ = 500 - 333\\ = \boxed{167}$ .

Ashish, Nice Question.:)

Abhay Tiwari - 5 years, 1 month ago

Jeez! Thanks. :)

Ashish Menon - 5 years, 1 month ago

Ashish, visit this :), hope you will love it. I have worked very hard for this problem.

Abhay Tiwari - 5 years, 1 month ago

@Abhay Tiwari – Clearly you have worked very hard. Rocking problem

Ashish Menon - 5 years, 1 month ago

@Ashish Menon – Thank you ;)

Abhay Tiwari - 5 years, 1 month ago

Set Operations right. So it must be combinatorics right?

Abhiram Rao - 5 years, 1 month ago

It is combinatorics, but I thought that Algebra would do well too ;)

Ashish Menon - 5 years, 1 month ago

NP.nice question though

Abhiram Rao - 5 years, 1 month ago

@Abhiram Rao – Ttthhhhhaaaaaaaaaaaanks :V

Ashish Menon - 5 years, 1 month ago

Since all numbers divisible by 4 are also divisible by 2, there will be no student that loves physics but not maths. This solution can be greatly simplified by ignoring the physics part.

250 students love maths, 166 students love chemistry. 83 love both, therefore 500 - (250 + 166 - 83 ) = 167 students love none of the subjects.

Pranshu Gaba - 5 years ago

Which topic do you like?

The answer is 167.

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