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Question
In the following number, replace * by the smallest number to make it divisible by 11:
1723*4
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Solution
1723*4
Sum of the digits at odd places 4+ 3+ 7= 14
Sum of the digits at even places *+2+1 = 3 + *
Difference = sum of odd terms – sum of even terms
= 14 – (3 + *)
= 11 − *
Now, (11 − *) will be divisible by 11 if * = 0.
i.e., 11 − 0 = 11
11 is divisible by 11.
∴ * = 0
Hence, the number is 172304.
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