How many two-digit numbers are divisible by 3?

Question

FirstInTest · Accepted Answer

Correct answer: A. Two-digit numbers range from 10 to 99.
The first two-digit number divisible by 3 is 12.
The last two-digit number divisible by 3 is 99.
This forms an arithmetic progression with first term $a = 12$, last term $l = 99$, and common difference $d = 3$.
The formula for the number of terms (n) in an arithmetic progression is $l = a + (n-1)d$.
$99 = 12 + (n-1)3$
$87 = (n-1)3$
$29 = n-1$
$n = 30$.
There are 30 two-digit numbers divisible by 3.

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