The number 611611611611 is:
(a)Divisible by both 6 and 11
(b)Divisible neither by 6 nor by 11
(c)Divisible by 6 only
(d)Divisible by 11 only
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. (d).
A number is divisible by 6 if it is divisible by both 2 and 3.
A number is divisible by 2 if its last digit is even.
The last digit of 611611611611 is 1, which is odd. Thus, the number is not divisible by 2.
However, since the number is not divisible by 2, it is not divisible by 6.
Odd places: 6 + 1 + 1 + 6 + 1 + 1 = 16
Even places: 1 + 6 + 1 + 6 + 1 + 1 = 16
Alternating sum: 16 - 16 = 0
Since the alternating sum is 0, the number 611611611611 is divisible by 11.
The given number is not divisible by 6 but is divisible by 11.
Therefore, the correct answer is (d) divisible by 11 only.