counting(general doubt)

Question

Q.1)How many positive integer less than 1000

a) are divisible by 7

b) are divisible by 7 but not by 11.

what should be the general approach to calculate this???

Comments

a )positive integer less than 1000 are divisible by 7 = $\left \lfloor \frac{1000}{7} \right \rfloor$ = 142

 

 b)  positive integer less than 1000 are divisible by  both 7  and  11 = $\left \lfloor \frac{1000}{lcm(7,11)} \right \rfloor$ = 12

therefore , positive integer less than 1000 are divisible by 7 but not by 11  = 142 - 12 = 130

---

thanks good explanation.i am finding criteria. for a number which is divisible by 7 what should be condition.Like a number which is divisible by 2 its last digit must be divisible by 2.