When 1985,6814 and 3741 are divided by the largest number x, the remainder is same in each case. What is the sum of the digits of x?

Correct option is C

Solution:

First, find the differences between the given numbers:

6814 - 1985 = 4829

6814 - 3741 = 3073

3741 - 1985 = 1756

The largest number x that divides each of these differences is the greatest common divisor (GCD) of 4829, 3073, and 1756.

Using the Euclidean algorithm, we find:

GCD(4829, 3073) = 439

GCD(439, 1756) = 439

Therefore, the largest number x is 439.

The sum of the digits of x is:

Sum of digits of 439 = 4 + 3 + 9 = 16