tracyyahoo wrote:
(2) 18=k*=36

Statement 2 suggests that 18 = 36.

Might be a problem with the way you transcribed the question

Cheers,
Brent

Here's how the question should be written:

For each positive integer n, the integer n* is defined by n*=(n^2)+1. What is the value of the positive integer k?
1. When k is divided by 4, the remainder is 1
2. 18 < k* < 36

Statement 1:
k can have several different values: k=1, k=5, k=9, etc
Statement 1 is not sufficient

Statement 2:
Here, we are told that 18 < (k^2) + 1 < 36
Subtract 1 from all 3 sides to get: 17 < (k^2) < 35
Since k is a positive integer, we can see that k must equal 5
As such, statement 2 is sufficient, and the answer is B

Cheers,
Brent