Question 104

How many natural numbers less than 1000 are divisible by 5 or 7 but NOT by 35?

Solution

Natural numbers less than 1000 divided by 5 are : 5,10,15,20,.....,990,995

=> Total numbers = $$\frac{(995-5)}{5}=198$$

Similarly, total numbers divided by 7 = $$\frac{(994-7)}{7}=141$$

and numbers divided by 35 = $$\frac{(980-35)}{35}=27$$

$$\therefore$$ Natural numbers less than 1000 are divisible by 5 or 7 but NOT by 35 = $$198+141-(2\times27)=285$$

=> Ans - (A)

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