Test the divisibility of each of the following numbers by 3:

(i) 83

(ii) 378

(iii) 474

(iv) 1693

(v) 60005

(vi) 67035

(vii) 591282

(viii) 903164

(ix) 100002

(i) 83

We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3.

Here, sum of digits is 11, which is not divisible by 3.

Hence, 83 is not divisible by 3.

(ii) 378

We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3.

Here, sum of digits is 18, which is divisible by 3.

Hence, 378 is divisible by 3.

(iii) 474

We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3.

Here, sum of digits is 15, which is divisible by 3.

Hence, 474 is divisible by 3.

(iv) 1693

We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3.

Here, sum of digits is 19, which is not divisible by 3.

Hence, 1693 is not divisible by 3.

(v) 60005

We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3.

Here, sum of digits is 11, which is not divisible by 3.

Hence, 60005 is not divisible by 3.

(vi) 67035

We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3.

Here, sum of digits is 21, which is divisible by 3.

Hence, 67035 is divisible by 3.

(vii) 591282

We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3.

Here, sum of digits is 27, which is divisible by 3.

Hence, 591282 is divisible by 3.

(viii) 903164

We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3.

Here, sum of digits is 23, which is not divisible by 3.

Hence, 903164 is not divisible by 3.

(ix) 100002

We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3.

Here, sum of digits is 3, which is divisible by 3.

Hence, 100002 is divisible by 3.