Question : The least number that must be subtracted from 1294 such that the obtained number when divided by 9, 11, and 13, leaves in each case the same remainder of 6, is:
Option 1: 2
Option 2: 3
Option 3: 1
Option 4: 4
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Correct Answer: 1
Solution : The LCM of 9, 11, and 13 is 1287. When 1294 is divided by 1287, the quotient is 1 and the remainder is 7. Here, we need the remainder in each case to be 6 and so, subtract (7 – 6) = 1 from 1294. Hence, the correct answer is 1.
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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:
Question : Find the least number which when divided by 12, 18, 24, and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Question : A number, when divided by 6, leaves a remainder of 3. When the square of the same number is divided by 6, the remainder is:
Question : M is the largest 4-digit number which, when divided by 4, 5, 6, and 7, leaves the remainder as 2, 3, 4, and 5, respectively. What will be the remainder when M is divided by 9?
Question : A number when divided by 221, leaves a remainder of 30. If the same number is divided by 13, the remainder will be:
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