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Question
How many two-digits numbers are divisible by 3?
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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 = 99
⇒ 12 + (n-1) × 3 =99 [an = a + (n-1) d]
⇒ 3n + 9 =99
⇒ 3n = 99 - 9 = 90
⇒ n = 30
Hence, there are 30 two-digit numbers divisible by 3.
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