There are 100 numbers between 300 and 1000 that are divisible by 7.
Finding the Solution
Several sources confirm this answer. The calculation involves finding the first and last numbers in the range divisible by 7, then using the concept of an arithmetic progression to determine the total count.
- First Number: The smallest number greater than or equal to 300 divisible by 7 is 301 (7 x 43).
- Last Number: The largest number less than or equal to 1000 divisible by 7 is 994 (7 x 142).
- Arithmetic Progression: The numbers divisible by 7 form an arithmetic sequence with a common difference of 7. The formula for the number of terms (n) in an arithmetic sequence is: n = (last term - first term) / common difference + 1. Therefore: n = (994 - 301) / 7 + 1 = 100
References Confirming the Answer
Multiple online resources, including Quora, Testbook, and various math forums, independently arrive at the same answer of 100. These resources explicitly state that there are 100 numbers between 300 and 1000 divisible by 7. For example, one source states: "∴ There are 100 numbers between 300 and 1000 which are divisible by 7."
