If r is the remainder when each of 7654, 8506, and 9997 is divided by the greatest number d (d > 1) then d - r is equal to = ?

Answer: Option A

d = HCF of (8506 - 7654), (9997 - 8506), (9997 - 7654)
= HCF of 852, 1491, 2343 = 213
$$\begin{array}{rl}& \text{213}\overline{)\text{ 7654 (}}35\\ & \frac{639}{1264}\\ & \frac{1065}{199}\\ & \text{Clearly r = 199}\\ & \therefore d-r=213-199\\ & =14\end{array}$$