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Question
How many two-digit numbers are divisible by 3?
Solution
The two digit numbers divisible by 3 are as follows:
12, 15, 18, 21, ...., 99
Clearly, this form an A.P with first term a = 12 and common difference d = 3
Last term = nth term = 99
The general term of an A.P. is given by
tn = a + (n – 1)d
`=>` 99 = 12 + (n – 1) × 3
`=>` 99 – 12 = 3n – 3
`=>` 87 = 3n – 3
`=>` 3n = 87 + 3
`=>` 3n = 90
`=>` n = `90/3` = 30
Thus, 30 two-digit numbers are divisible by 3.
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