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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 divihttps://cracku.in/cms/questions/edit/458991#sible 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.
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