Discussion
If a number 5a108 is completely divisible by 11, then the value of 'a' will be :
Answer: C
The value of a is 3.
A number is divisible by 11 when the difference between the sum of its digits in odd places and the sum in even places is 0 or a multiple of 11. For 5a108, the odd-place digits are 5, 1 and 8 and the even-place digits are a and 0:
\[ \begin{aligned} (5 + 1 + 8) - (a + 0) &= 14 - a \\ 14 - a = 11 &\Rightarrow a = 3 \end{aligned} \]
Check: 53108 = 11 × 4828. With a = 1, 2 or 4 the difference is 13, 12 or 10, none of which is a multiple of 11.
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