How many 3-digit numbers are completely divisible 6 ?

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Question

How many 3-digit numbers are completely divisible 6 ?

Options:

A . 149

B . 150

C . 151

D . 166

Answer: Option B

3-digit number divisible by 6 are: 102, 108, 114,... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then t_n = 996.

a + (n - 1)d = 996

102 + (n - 1) x 6 = 996

6 x (n - 1) = 894

(n - 1) = 149

n = 150

Number of terms = 150.

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