A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over. What is the sum of the two smallest possible values of n?
Choices:
A) 54 B) 58 C) 62 D) 66 E) 70
n = 4k+1 = 7j+3   Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+3.   1, 5, 9, 13, 17 = 7(2)+ 3   The next such number is 17 + 4*7= 
<gadget id="calculator">17 + 4*7</gadget>
<output>45</output>
45.   17+45= 
<gadget id="calculator">17+45</gadget>
<output>62</output>
62   The answer is 62.
<result>C</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 3 students left over. What is the sum of the two smallest possible values of n?