A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 4 students left over. What is the sum of the two smallest possible values of n? Select the correct option:
A) 66
B) 70
C) 74
D) 78
E) 82

Rationale: "n = 4 k + 1 = 7 j + 4 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 4 . 1 , 5 , 9 , 13 , 17 , 21 , 25 = 7 ( 3 ) + 4 the next such number is 25 + 4 * 7 = 53 . 25 + 53 = 78 the answer is d ."
Answer: D