JEE Main 2020 · Mathematics · Sets, Relations and Functions · medium

Among the integers from 1 to 200, the number of integers that are divisible by 2 or by 3 but are not divisible by 5 is

Single correct option

Among the integers from

1

200

, the number of integers that are divisible by

2

or by

3

but are not divisible by

5

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Answer: (B) $106$

Let

A

be the multiples of

2

B

the multiples of

3

. Then

|A|=100

|B|=66

|A\cap B|=\lfloor 200/6\rfloor=33

, so

|A\cup B|=100+66-33=133

. Now remove those that are also multiples of

5

. Multiples of

10

up to

200

20

; multiples of

15

13

; multiples of

30

6

. So the multiples of

5

inside

A\cup B

number

20+13-6=27

. The required count is

133-27=106

. The trap is stopping at

133

, which ignores the condition on

5

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