How many positive integers between 200 and 300 (both inclusive) are no

total integers = 300-200+1 ; 101
+ve integers divisible by 2 = 51
integers divisible by 3 = 34
integers divisible by 5 = 21

integers divisible by both 2& 3 = half of integers divisible by 3 ' ie even integers divisible by 3' ; 17
integers divisible by both 2& 5 = half of integers divisible by 5 ' ie even integers divisible by 5'; 11
integers divisible by 3 & 5 both = 225,255,285 ; 3

so total integers divisible by 2,3 & 5 = (51-17-11)+ ( 34-3) + 21 = 75
integers not divisible by 2,3,5 would be 101- 75 = 26
IMO D

Total numbers: 300 - 200 + 1 = 101

Total numbers divisible by 2: First [200] and Last [300]

=> 300 = 200 + (n-1)2
=> 102 = 2n
=> n = 51

Total numbers divisible by 3: First [201] and Last [300]

=> 300 = 201 + (n-1)3
=> 102 = 3n
=> n = 34

Total numbers divisible by 5: First [200] and Last [300]

=> 300 = 200 + (n-1)5
=> 105 = 5n
=> n = 21


Total numbers divisible by 6[LCM of '2' and '3']: First [204] and Last [300]

=> 300 = 204 + (n-1)6
=> 102 = 6n
=> n = 17

Total numbers divisible by 6[LCM of '3' and '5']: First [210] and Last [300]

=> 300 = 210 + (n-1)15
=> 105 = 15n
=> n = 7

Total numbers divisible by 10[LCM of '2' and '5']: First [200] and Last [300]

=> 300 = 200 + (n-1)10
=> 110 = 10n
=> n = 11

Total numbers divisible by 30[LCM of '2', '3' and '5']: First [210] and Last [300]

=> 300 = 210 + (n-1)30
=> 120 = 30n
=> n = 4

Total numbers not divisible by '2' , '3' or '5': 101 - 51 - 34 - 21 + 17 + 7 + 11 - 4 = 26

Answer D

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