A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 2 students left over. What is the sum of the two smallest possible values of n? Choose one:
A) 33  B) 46  C) 49  D) 54  E) 86
n = 4k+1 = 5j+2   Let's start at 1 4 +1= 
<gadget id="calculator">4 +1</gadget>
<output>5</output>
5j+2   Let's start at 1= 4(0)+1 and keep adding 4 until we find a number in the form 5j+2.   1, 5, 9, 13, 17 = 5(3)+2   The next such number is 17 + 4*5= 
<gadget id="calculator">17 + 4*5</gadget>
<output>37</output>
37.   17+37= 
<gadget id="calculator">17+37</gadget>
<output>54</output>
54   The answer is 54.
<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 5 with 2 students left over. What is the sum of the two smallest possible values of n?