If the five-digit number abcde is divisible by 6, then which of the following numbers is not necessarily divisible by 6?

Given abcde is divisible by 6.

Number is divisible by 6 only if it is divisible by both 2 & 3. This implies abcde is divisible by both 2 & 3. 

abcde is divisible by 2 only if 'e' is even number = {0,2,4,6,8}

abcde is divisible by 3 only if "a+b+c+d+e = 3(k) " that is sum of digits is multiple of 3.

Now , lets evaluate the following :

Option A : eee - divisible by 6:

1. 'e' is even number so, it is divisible by 2. 

2. sum of digits is '3(e)' which is multiple of 3, so it is divisible by 3.

Option B : edcba - may/may not divisible by 6

1. The number is ending with 'a' which can be either even or odd, Hence may/may not be divisible by 2.

2. The sum of digits is "a+b+c+d+e" which is equal to 3(k) as deduced above, hence always divisible by 3.

Option C : cdbae - divisible by 6 :

1. Number is ending with 'e' which is even number, hence always divisible by 2.

2. The sum of digits is "a+b+c+d+e" which is equal to 3(k) as deduced above, hence always divisible by 3.

Option D : bbadcacede - divisible by 6 :

1. Number is ending with 'e' which is even number, hence always divisible by 2.

2. The sum of digits is "2(a+b+c+d+e)" which is equal to 6(k) as deduced above, hence always divisible by 3.

Therefore, Option B - 'edcba' need not necessarily be divisible by 6.