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,
an = a + (n - 1) x d..........(1)
here, an 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.
Refer to divisibility rule of 7 to know more about divisibility rules.
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