Understanding Divisibility Rules
To determine the divisibility of numbers based on the sum of their digits, we can apply specific rules. In this case, we focus on the sum being 27.
Divisibility by 9
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- Since the sum of the digits is 27, we can check:
- 27 ÷ 9 = 3, which is an integer.
- Thus, any number with a digit sum of 27 is divisible by 9.
Divisibility by 6
- A number is divisible by 6 if it is divisible by both 2 and 3.
- While a sum of 27 indicates divisibility by 3, we cannot conclude anything about evenness (divisibility by 2) without knowing the last digit.
- Therefore, we cannot confirm divisibility by 6.
Divisibility by 11
- A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum in even positions is either 0 or divisible by 11.
- The sum of the digits alone (27) does not provide enough information to check this rule.
Divisibility by 7
- The divisibility rule for 7 involves more complex calculations or specific checks on the number itself.
- Again, without the actual number, we cannot ascertain divisibility by 7.
Conclusion
In summary, the only definitive conclusion we can draw from a digit sum of 27 is that the number is divisible by 9. Thus, option 'B' is the correct answer.