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How many three-digit numbers are divisible by 9?

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100

answer is A.

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Detailed Solution

The three-digit numbers divisible by 9 are 108,117,126,...,999.
Thus,

a = 108 and,

d = 117 − 108 ⇒ d = 9

T n = 999

Formula for the nth term:

T n = a + n − 1 × d

Applying,

108 + (n − 1) × 9 = 999 ⇒ 9 n + 99 = 999 ⇒ 9 n = 999 − 99 ⇒ 9 n = 900

⇒ n = 9009 ⇒ n = 100

Therefore, there are 100 three-digit numbers divisible by 9.
Hence, option (1) is correct.

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