Question : The sum of the digits of the least number which when divided by 36, 72, 80 and 88 leaves the remainder 16, 52, 60 and 68, respectively, are:
Option 1: 17
Option 2: 11
Option 3: 14
Option 4: 16
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Correct Answer: 16
Solution :
In this case, the differences between the divisors and the respective remainders are the same (20) for all four cases.
Therefore, the least number is given by LCM(36, 72, 80, 88) – 20.
The LCM of 36, 72, 80, and 88 is 7920.
Therefore, the least number = 7920 – 20 = 7900
The sum of the digits of this number = 7 + 9 + 0 + 0 = 16
Hence, the correct answer is 16.
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