Question

How many numbers exist between 100 and 1000 which are divisible by 7?

Answer 1

In a number, double the last digit and subtract it from all the other digits in the original number excluding the final digit. If the answer is either 0 or a number divisible by 7, then the original number is also divisible by 7.

Following this rule,

Total number of numbers divisible by 7 up to 1,000 = 142

Total number of numbers divisible by 7 up to 100 = 14

Thus, the total number of numbers between 100 and 1,000 divisible by 7 is 142 - 14 = 128.

The first number in this series is 105 and the last number is 994.

Answer 2

Solution :-

Numbers between 100 and 1000 which are exactly divisible by 7.

⇒ 100/7 = 14.28 < 15

⇒ 1000/7 =  142.85 > 142

Hence, the numbers which are exactly divisible by 7 are -

1st number = 7*15 = 105
2nd  = 7*16 = 112
3rd   = 7*17 = 119 .....................and so on till 142*7 = 994

Hence, 142 - 14 = 128

There are total 128 numbers which are exactly divisible by 7 between 100 and 1000.