1. Is the number completely divisible by 99? I. The number is divisible by 9 and 11 simultaneously. II. If the digits of the number are reversed, the number is divisible by 9 and 11.
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- By: anil on 05 May 2019 02.32 am99 = 9 * 11 => If the number is divisible by 9 and 11, then the number is divisible by 99. => We can answer the question using only statement I. The divisibility rule of 9 is that the sum of the digits in the number must be divisible by 9. The divisibility rule of 11 is that the difference of sums of digits in odd places and digits in even places must be a multiple of 11. According to statement II, if the number is reversed then the number is divisible by 9 and 11 => Divisible by 99. Now, on reversing the number again, the number is still divible by 99 because the sum of the digits remains the same and also the difference of sums of digits in odd places and digits in even places remains the same. Hence, the question can be answered using either of the statements alone.
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Conditions :
(i) If the first digit is odd and the last digit is even, the codes for the first and last digits are to be interchanged.
(ii) If both the first and the last digits are even, both are to be coded as *.
(iii) If both the first and the last digits are odd, both are to be coded as $.215349