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

Question of The Day27-12-2021

How many natural numbers are there between 100 and 1000 that are divisible by 7?

Answer

Correct Answer : c ) 128

Explanation :

As we can see the first number divisible by 7 between 100 and 1000 is 105.

Now the next number will be 105 + 7 = 112, 112 + 7 = 119 and so on.

The last number divisible by 7 between 100 and 1000 will be 994.

So, here we have got an arithmetic progression (A.P.) with:

105 as first term (a)

7 as common difference (d), and

994 as last term (l)

Let n be the total number of terms in the series.

We know that,

a_n = a + (n - 1) x d..........(1)

here, a_n is l = 994.

We need to find the number of terms.

Putting in eq. (1)

994 = 105 + (n - 1) x 7

994 - 105 = (n - 1) x 7

889 = (n - 1) x 7

889/7 = n - 1

127 = n - 1

n = 128

Hence, (c) is the correct answer.

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