Question : Let $x$ be the smallest number which, when added to 2000, makes the resulting number divisible by 12, 16, 18, and 21. The sum of the digits of $x$ is:
Option 1: 7
Option 2: 5
Option 3: 6
Option 4: 4
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Correct Answer: 7
Solution :
LCM of (12, 16, 18, 21) = 1008 (less than 2000)
The next number which is divisible by 12, 16, 18, and 21= (2 × 1008) = 2016
Also, 2016 is 16 more than 2000.
So, (1 + 6) = 7
Hence, the correct answer is 7.
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