Correct option is A
Given:
The numbers are 8667, 8022, and 7807
We need to find the greatest number x that divides these numbers, leaving the same remainder in each case, and then calculate the sum of the digits of x
Concept Used:
The value of xx is the Highest Common Factor (HCF) of the absolute differences between these numbers.
According to the property:
K = HCF [|a - b|, |b - c|, |c - a|]
Solution:
x = HCF[|8667 - 8022|, |8022 - 7807|, |8667 - 7807|]
Absolute differences between the numbers:
|8667 - 8022| = 645
|8022 - 7807| = 215
|8667 - 7807| = 860
Now, the HCF of the differences: 645, 215, and 860
HCF = 215
The greatest number x is 215
Sum of digits of 215 = 2 + 1 + 5 = 8