Find all possible values of x for which the 4-digit number 320x is divisible by 3.

Question:

Find all possible values of x for which the 4-digit number 320x is divisible by 3. Also, find the numbers.

Solution:

If a number is divisible by 3, then the sum of the digits is also divisible by 3.

$3+2+0+x=5+x$ must be divisible by 3 .

This is possible in the following cases:

(i) $x=1$

$\therefore 5+x=6$

Thus, the number is 3201 .

(ii) $x=4$

$\therefore 5+x=9$

Thus, the number is 3204 .

(iii) $x=7$

$\therefore 5+x=12$

 

Thus, the number is 3207 .

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