JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Sets Relations and Functions

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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:

(A)102
(B)42
(C)1
(D)38✓ Correct

Answer: (D)

Solution

Count the opt-ins with inclusion and exclusion. Multiples of

2

number

70

, of

3

number

46

, of

5

number

28

; the pairwise overlaps, multiples of

6

10

and

15

, number

23

14

and

9

; and multiples of

30

number

4

. So those taking at least one course total

70 + 46 + 28 - 23 - 14 - 9 + 4 = 102

. Out of

140

students, the ones taking none are

140 - 102 = 38

JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Single correct option

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