Answer:
6
Step-by-step explanation:
This question could have simply been asking for the integers between 20 and 88 since the numbers from 10-19 do not have both digits even, same goes for 89 and 90.
So Looking at the remaining numbers we can immediately ignore all numbers with the first digit odd leaving only a quite limited set of numbers to examine. Let A be the set of these numbers.
A = {20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88}
But for the number to be divisible by 3, it means that the sum of the digits must be divisible by 3. And since the sum of two even numbers is even, it must also be even (divisible by 2), meaning the sum of the digits must be be divisible by 6. This only happens when the sum of the digits are 6 or 12 (on the interval 2-16 where 2 is the smallest possible sum of two digits on the set A and 16 is the largest possible sum).
Using this information we can easily find what numbers match these requirements.
{24, 42, 48, 60, 66, 84}
The set has 6 elements
