If p and q are positive integers each greater than 1, and 17(p+1)=25(q+1), what is the least possible value of p+q?  Choose the correct option: A) 36 B) 42 C) 40 D) 46 E) none

Rationale: "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 25 , so the least value of p is 24 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 24 + 16 = 40 . answer : c ."
Answer: C