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# 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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