When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 39, what is the remainder when k is divided by 7?
Choose the correct choice from the following.
A) 4 B) 5 C) 6 D) 3 E) 7

Rationale: cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 39 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 39 ) 17 is the only common number in both the sets . hence k = 17 answer : d
Answer: D