What is the number of natural numbers less than or equal to 1000 and divisible by 5 or 7?

Correct option is A

Given:
Maximum limit = 1000
Divisors = 5 and 7
Formula Used:
Number of multiples of n up to M = Integer part of $$(\frac{M}{n})$$​​
​$$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$​​
Solution:
Let A be the set of numbers divisible by 5, and B be the set of numbers divisible by 7.
The intersection of A and B represents numbers divisible by both 5 and 7 (i.e., LCM of 5 and 7 = 35).
Count of numbers divisible by 5:
​$$n(A) = \frac{1000}{5} = 200$$​​
Count of numbers divisible by 7:
​$$n(B) = \frac{1000}{7} = 142.85 \approx 142$$​​
Count of numbers divisible by 35:
​$$n(A \cap B) = \frac{1000}{35} = 28.57 \approx 28$$​​
Total numbers divisible by 5 or 7:
​$$n(A \cup B) = 200 + 142 - 28$$​​
​$$= 342 - 28 = 314$$​​
Final Answer
So the correct answer is (a)