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Find how many 3-digit numbers are divisible by $6$ in all?

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149

150

151

166

answer is B.

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Detailed Solution

The 3-digit numbers divisible by 6 are

102, \dots, 315, 324, \dots, 996

.
The given series forms the AP.
nth term of an A.P. is calculated using,

a n = a + n − 1 d … 1

a = 102

d = 6

a_{n} = 996

⇒ 996 = 102 + n − 1 6

⇒ 996 − 102 = n − 1 6

⇒ 894 = n − 1 6

⇒ n − 1 = 8946

\Rightarrow n - 1 = 149

\Rightarrow n = 149 + 1

\Rightarrow n = 150

Hence, the required answer is 150.
Therefore, option 2 is correct.

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