Question 133

If A381 is divisible by 11 , find the value of the smallest natural number A

Solution

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For any number to be divisible by 11, the difference between the sum of digits at odd and even positions should be a multiple of 11.
Sum of odd position digits = A + 8
sum of even position digits = 3 + 1 = 4.
Their difference i.e. A+8 - 4 = A+4 should be a multiple of 11. So, the smallest value that A can take for which A+4 is a multiple of 11 is 7 i.e. Option D.

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