Question : The number 1563241234351 is:
Option 1: divisible by 11 but not by 3
Option 2: neither divisible by 3 nor by 11
Option 3: divisible by both 3 and 11
Option 4: divisible by 3 but not by 11
Correct Answer: neither divisible by 3 nor by 11
Solution : The sum of the digits of the number 1563241234351 $=1\ +\ 5\ +\ 6\ +\ 3\ +\ 2\ +\ 4\ +\ 1\ +\ 2\ +\ 3\ +\ 4\ +\ 3\ +\ 5\ +\ 1$ $= 40$ As we know, 40 is not divisible by 3 so the number is not divisible by 3. Now check divisibility rule 11 $(5\ +\ 3\ +\ 4\ +\ 2\ +\ 4\ +\ 5) -\ (1\ +\ 6\ +\ 2\ +\ 1\ +\ 3\ +\ 3\ +\ 1)$ $=23\ - 17$ $ =6$ As we know, 6 is not a multiple of 11. So, the number is neither divisible by 3 nor 11. Hence, the correct answer is neither divisible by 3 nor by 11.
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