Is the given statement true or false ?

A four-digit number is divisible by 3. The number is rearranged as . Is the second number divisible by 3?

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True

False

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Detailed Solution

The given statement is true.
Concept- Numbers in the form

mean that each digit is displayed individually with the variable. If the sum of all digits in a number is divisible by 3, then the rule of divisible 3 is used to indicate that the number itself is divisible by 3.
It is stated in the question that the number

' is completely divisible by 3. This means that the number

meets the divisor rule of 3. According to the law of divisor of 3, if the sum of all digits of a number is divisible by 3, then the number itself is divisible by 3. This means that

is also divisible by 3. So if you rearrange the numbers as the sum of the numbers,

, the numbers will be

, which is the same value as (a + b + c + d). Therefore, the second number

is also divisible by 3. This is because it meets the rule of splitability of 3.
Hence, the correct answer is option (1).

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