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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Question : Let $x$ be the least number which, when divided by 5, 6, 7, and 8, leaves a remainder of 3 in each case, but when divided by 9, leaves no remainder. The sum of the digits of $x$ is:
Option 1: 21
Option 2: 22
Option 3: 18
Option 4: 24
Question : If the sum of digits of any number between 100 and 1000 is subtracted by the same number, the resulting number is always divisible by:
Option 1: 2
Option 4: 9
Question : What is the smallest number which can be added to 9454351626 so that it becomes divisible by 11?
Option 1: 1
Option 2: 6
Option 3: 5
Question : Which of the following is the smallest ratio? $\frac{5}{6}, \frac{7}{9}, \frac{11}{12}, \frac{13}{18}$
Option 1: $\frac{7}{9}$
Option 2: $\frac{13}{18}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{11}{12}$
Question : The arithmetic mean of the following numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7 is:
Option 1: 4
Option 3: 14
Option 4: 20
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