What is the largest positive integer 'n' for which there is a unique integer k such that 8/15 < n/(n+k) < 7/13 ? a) 112 b) 62 c) 125 d) 216 (explain how)

Question

Answer 1

15/8>(n+k)/n>13/7
7/8>k/n>6/7
49/56>k/n>48/56
Since k is an unique integer,
98/112>k/n>96/112
k = 97 and n = 112

Answer 2

15/8>(n+k)/n>13/7
7/8>k/n>6/7
49/56>k/n>48/56
Since k is an unique integer,
98/112>k/n>96/112
k = 97 and n = 112