Answer:
option 3: 357 numbers.
Explanation:
1. Divisibility by 2 or 7: We are looking for numbers till 500 that are completely divisible by either 2 or 7. This means we need to find the count of numbers that are divisible by 2, divisible by 7, or divisible by both 2 and 7.
2. Divisible by 2: Every even number is divisible by 2. To find the count of even numbers till 500, we can divide 500 by 2, which gives us 250. So, there are 250 even numbers till 500.
3. Divisible by 7: To find the count of numbers divisible by 7 till 500, we divide 500 by 7, which gives us 71.4285714286. Since we are counting whole numbers, we can round down to 71. So, there are 71 numbers divisible by 7 till 500.
4. Divisible by both 2 and 7: To find the count of numbers divisible by both 2 and 7, we need to find the count of numbers divisible by their least common multiple, which is 14 (2 x 7). We divide 500 by 14, which gives us 35.7142857143. Rounding down to the nearest whole number, we have 35 numbers divisible by both 2 and 7 till 500.
5. Total count: To find the total count of numbers divisible by 2 or 7, we add the count of even numbers (250), the count of numbers divisible by 7 (71), and the count of numbers divisible by both 2 and 7 (35). 250 + 71 + 35 = 356.