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How many three digit numbers are divisible by 7?

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128

120

121

122

answer is A.

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Detailed Solution

We need to find the number of three digit numbers divisible by 7.
We know the formula,

a n = a + n − 1 d

Where,
The first term is a.
The common difference is d.
The number of terms are n.
The list of three-digit numbers divisible by seven is, 105,112,119,...,994
This forms an arithmetic progression of the form

a n = a + n − 1 d

, where a is the first term,

a n

is the

n t h

term and d is the common difference between the terms.
Thus in the case of the sequence 105,112,119,...,994.

a = 105 a n = 994 d = 7

Substitute 105 for a , 994 for

a n

and 7 for d in the equation

a n = a + n − 1 d

994 = 105 + n − 1 7 ⇒ 889 = n − 1 7 ⇒ n = 8897 + 1 ⇒ n = 128

Thus there are 128 three-digit numbers that are divisible by seven.
Therefore, option 1 is correct.

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