How many brothers?

Genesis 42:3 says, “And Joseph's ten brethren went down to buy corn in Egypt. 42:4 But Benjamin, Joseph's brother, Jacob sent not with his brethren; for he said, Lest peradventure mischief befall him.”  So, Jacob sent ten of his sons to buy corn in Egypt.  Genesis 42:13 says, “And they said, Thy servants are twelve brethren, the sons of one man in the land of Canaan; and, behold, the youngest is this day with our father, and one is not.”  Why would you say there are 12 of you when there are 10 before the Egyptian Governor and only one at home?  Remember, they brought the blood dipped coat of many colors to Jacob, Genesis 37:33 “And he knew it, and said, It is my son's coat; an evil beast hath devoured him; Joseph is without doubt rent in pieces.”  So if you are lying about your brother being dead why to you count him in your group.  Sounds, to me, like he is just trying to make the story work.