Given that the number $\overline{35a64}$ is divisible by 3, where $a$ is a digit, what are the possible values of $a$?
Given:
Given that the number $\overline{35a64}$ is divisible by 3, where $a$ is a digit.
To do:
We have to find the possible values of $a$.
Solution:
The number $\overline{35a64}$ is divisible by 3.
This implies,
The sum of its digits will also be divisible by 3.
Therefore,
$3 + 5 + a + 6+ 4$ is divisible by 3.
$18 + a$ is divisible by 3
18 is divisible by 3.
This implies,
$a$ is divisible by 3.
Therefore,
The values of $a$ can be $0, 3, 6, 9$.
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