A symmetric number of an another one is a number where the digit are reversed. For instance, 123 is the symmetric of one of 321. Thus the difference of a number and its symmetrical must be divisible by which of the following?  Choose the most appropriate option.
A) 4 B) 5 C) 6 D) 7 E) 9
Let's consider the example of three digit symmetric numbers {abc} and {cba}. Three digit number can be represented as: {abc}=100a+10b+c and {cba}=100c+10b+a. The difference would be:   {abc}-{cba}=100a+10b+c-(100c+10b+a)=99a-99c=99(a-c).   Two digit: {ab} and {ba}. {ab}-{ba}=10a+b-(10b+a)=9a-9b=9(a-b)   Hence the difference of two symmetric numbers (2 digit, 3 digit, ...) will always be divisible by 9.   Answer: 9.
<result>E</result>
A symmetric number of an another one is a number where the digit are reversed. For instance, 123 is the symmetric of one of 321. Thus the difference of a number and its symmetrical must be divisible by which of the following?