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?
Option 1: 2
Option 2: 1
Option 3: 3
Option 4: 6
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Correct Answer: 1
Solution : The least common multiple (LCM) of 4, 5, 6, and 7 is 420. The required largest 4-digit number will be a multiple of 420. Remainder of $\frac{9999}{420}$ is 339. The largest 4-digit number will be 9999 – 339 = 9660 which is divisible by 4, 5, 6, and 7. Now, as given, when the number is divided by 4, 5, 6, and 7, it leaves 2, 3, 4, and 5 as remainders. The difference between each divisor and the remainder is 2, as shown below.
Hence, the required number is 9660 – 2 = 9658 When 9658 is divided by 9, it will leave the remainder 1. Hence, the correct answer is 1.
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Question : N is the largest two-digit number which, when divided by 3, 4, and 6, leaves the remainder of 1, 2, and 4, respectively. What is the remainder when N is divided by 5?
Question : The largest five-digit number which when divided by 7, 9, and 11, leaves the same remainder as 3 in each case, is:
Question : A number $n$ when divided by 6, leaves a remainder of 3. What will be the remainder when $\left(n^2+5 n+8\right)$ is divided by 6?
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 : 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:
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