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Question

Choose the correct answer in each of the following questions:

How many two-digit numbers are divisible by 3? [CBSE 2012]

(a) 25 (b) 30 (c) 32 (d) 36

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Solution

The two-digit numbers divisible by 3 are 12, 15, 18, ..., 99.

Clearly, these number are in AP.

Here, a = 12 and d = 15 − 12 = 3

Let this AP contains n terms. Then,

an=9912+n-1×3=99 an=a+n-1d3n+9=993n=99-9=90
n=30

Thus, there are 30 two-digit numbers divisible by 3.

Hence, the correct answer is option is B.

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