For a lottery ticket, Emily chose six numbers that average

There is two built in results.
1)If this is a lottery ticket; I think problem implies that the numbers are different.
2)the sum of numbers is 60.
Problem asks that 3 or more numbers are 2 digited?

Then lets look at to statements.
1)one of the numbers is 10.
So the others sum to 50. The numbers can be 1,2,3,4,40 or 5,9,11,12,13 So insuff.

2)3 of numbers sums to 40. This is same as the other 3 sums to 20. This is insuff too. Because one can choose numbers like that.
1,2,37,5,7,8 or 10, 11, 19 and 12, 5, 3. so insuff.

together
we know that one of the numbers is 10. But there are 2 possibilities. 10 may be in the numbers that sum to 40 or not.
in first possibility, lets assume 10 in the first three, the other two numbers sum to 30. At least one of the other two is two digited. But it is not mandatory that two of them are two digited. But we know that at least 2 of 3 are two digited (10 and one of the other two). Lets look at the 3 other numbers that sum to 20. There need not be a number that is greater than 10. So insuff.

E

Lottery means that numbers are distinct and totals to 60...

1.
10 + 1 + 2 + 3 + 4 + 40 = 60, or... (2 two-digits)
10 + 11 + 12 + 13 + 8 + 6 = 60 ... (more than 3 two-digits)
INSUFFICIENT!

2.
10 + 11 + 19 + 14 + 6 = 60 (more than 3 two-digits)
10 + 21 + 9 + 9 + 11 = (not more than 3 )
INSUFFICIENT!

Together (1) and (2)
Samples of statement 2 shows still that it's insufficient

Answer: E