The only way for (3x + 1)/10 to have a remainder of 0 would be if 3x has a units digit of 9, so that when you add 1 to it you get a mulitple of 10. So x=3, 13, 23, etc would do it.
Statement 2 is obviously not sufficient by itself, as x would work for 13, but not for say 10 for example.
Statement 1 gives a way to determine x. If you try n=1 it doesn't work and you have x>4. So you know that statement 2 doesn't add any value and your answer must be A or E. Now you have to try and see if there is a case where it would work. If you can find a case where it does work using statement 1 then your answer is E, if you can't find a case where it works then your answer is A, as statement 1 would tell you that (3x+1)/10 does not have a remainder of 0.
In order for it to work you need x to have a units digit of 3. So 3n+2 must have a units digit of 3. Because you are adding 2 you need 3n to have a units digit of 1. This occurs when x=7 because 7*3=21.
70/10 has a remainder of 0
So the answer must be E.