In the following question, a number is coded as two digits, where: The first digit is the remainder when the number is divided by 7. The second digit is the remainder when the number is divided by 11. That is, if a number N is divided by 7 and gives remainder a, and by 11 and gives remainder b, then the code is a, b. Example: If N = 53 53 ÷ 7 = 7 remainder 4 53 ÷ 11 = 4 remainder 9 So, the code is 4, 9 Which is the least two-digit number with the code 4, 4 in this coding system?
81
Code 4, 4 means the number leaves remainder 4 when divided by 7 and also remainder 4 when divided by 11.
So N – 4 is divisible by both 7 and 11, that is, by LCM(7, 11) = 77.
So N = 77k + 4, giving 4, 81, 158, …
4 is a single-digit number, so the least two-digit number with this code is 77 + 4 = 81.
Check: 81 ÷ 7 = 11 remainder 4 and 81 ÷ 11 = 7 remainder 4, while 88 ÷ 11 leaves 0, 85 ÷ 7 leaves 1 and 89 ÷ 7 leaves 5.
Hence, 81.
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Important Questions from Coding Decoding Based on Numbers
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If in a certain code, 6723 is coded as 8901, how is 2435 coded in that language?
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