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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


Team Careers360 14th Jan, 2024
Answer (1)
Team Careers360 15th Jan, 2024

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.

Divisor Remainder Difference
4 2 2
5 3 2
6 4 2
7 5 2

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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