A number in which each digit except 0 appears exactly 3 times is divisible by 3.

Question

A number in which each digit except 0 appears exactly 3 times is divisible by 3. For example, 777, 555, 222 and 414, 143, 313 are divisible by 3. Explain why this is true. Choose the correct answer below A. Suppose a number n has the digits a, b, c, ..., m repeated exactly 3 times. Then the number of digits in the number will be a multiple of 3. By the divisibility test for 3, this implies that 3/n. B. Suppose a number n has the digits a, b, c, ..., m repeated exactly 3 times. Since there are nine unique digits that are not 0, nine of these digits a, b, c, ..., m will be non-zero digits, and 9 is a multiple of 3. By the divisibility test for 3 this implies that 3/n. c. Suppose a number n has the digits a, b, c, ..., m repeated exactly 3 times. Then the sum of the digits is 3a + 3b + 3c +... + 3m or 3(a + b + c +... + m). By the divisibly test for 3, this implies that 3/n. d. Suppose a number n has the digits a, b, c, ..., m repeated exactly 3 times. Then the sum a + b + c, ... + m will be a multiple of 3. By the test for 3, this implies that 3/n.

Explanation / Answer

Answer will be Option (C)
A number is divisble by 3 only if the sum of a number is divisible by 3.
Here in the question sum of total number is divisble by 3 which is explained in option C.

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