How many number are there from 500 to 650 (including both) which are neither divisible by 3 nor by 7?

87

Total no. b/w 650 and 500 (D)= 650 - 499 =151

Tota no. b/w 650 and 500 which divisible by 3: 

= \(\frac{650}{3}\) - \(\frac{500}{3}\) = 216 - 166 = 50

Tota no. b/w 650 and 500 which divisible by 7 = \(\frac{650}{7}\) - \(\frac{500}{7}\) =   92 - 71  = 21

Tota no. b/w 650 and 500 which divisible by 3 & 7 both = \(\frac{650}{3 × 7}\) - \(\frac{500}{3 × 7}\) = 30 - 23 = 7

D = 151 -50 -21 +7 = 87