The largest 4 digit number that leaves the same remainder when divided by 2, 3, 4 and 5 is

We know that the number leaves the same remainder when divided by 2,3,4 and 5.
Therefore, the number should be of the form LCM(2,3,4,5) + k.
LCM of 2,3,4,5 is 60.
The largest multiple of 60 below 10,000 is 9960.
2 can leave a remainder of 0 or 1.
Therefore, the largest possible value of k is 1.
The largest 4 digit number that leaves the same remainder when divided by 2, 3, 4 and 5 is 9960 + 1 = 9961.

Therefore, option D is the right answer.