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 = ?
A. 14
B. 18
C. 24
D. 28
Answer: Option A
Solution(By Examveda Team)
d = HCF of (8506 - 7654), (9997 - 8506), (9997 - 7654)= HCF of 852, 1491, 2343 = 213
$$\eqalign{ & {\text{213}}\overline {){\text{ 7654 (}}} 35 \cr & \,\,\,\,\,\,\,\,\,\,\frac{{639}}{{{\text{ }}1264}} \cr & \,\,\,\,\,\,\,\,\,\,\frac{{{\text{ }}1065}}{{{\text{ }}199}} \cr & {\text{Clearly r = 199}} \cr & \therefore d - r = 213 - 199 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 14 \cr} $$
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