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? Choices
A) 66  B) 70  C) 74  D) 78  E) 82
n = 4k+1 = 7j+4   Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+4.   1, 5, 9, 13, 17, 21, 25 = 7(3)+ 4   The next such number is 25 + 4*7= 
<gadget id="calculator">25 + 4*7</gadget>
<output>53</output>
53.   25+53= 
<gadget id="calculator">25+53</gadget>
<output>78</output>
78   The answer is 78.
<result>D</result>
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?