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In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is

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102

answer is D.

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Detailed Solution

$L e t M d e n o t e s M a t h s$

$P d e n o t e s P h y s i c s$

$C d e n o t e s C h e m i s t r y$

$n (M) = 70 n (P) = 46 n (C) = 28$

$n (M \cap P) = 23; n (P \cap C) = 9$

$n (m \cup P \cup C) > 102$

$N o . o f s t u d e n t s n o t o p t e d f o r a n y c o u r s e = 140 - 102 = 38$

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