Does (1,1) lie on line q?
Statement 1:
Slope of q is not 1.
There are infinitely many lines whose slopes are not 1, and they can or cannot pass through (1,1).
Thus, (1,1) can or cannot lie on line q.
For eg: i. (1,1) lies on line x = 1 having slope \(\neq\) 1
ii. (1,1) does not lie on line x = 2 having slope \(\neq\) 1
Statement 1 is Not Sufficient.
Statement 2:
Line q does not pass through (0,0)
There are many lines, which do not pass through (0,0), and they can or cannot pass through (1,1).
Thus, (1,1) can or cannot lie on line q.
Examples in Statement 1 can be considered here [line x = 1 and line x = 2].
Statement 2 is also Not Sufficient.
Statement 1 and Statement 2 combined:
Slope of q is not 1 and Line q does not pass through (0,0).
There are infinitely many lines, whose slope is not 1 and which do not pass through (0,0), and they can or cannot pass through (1,1).
Thus, (1,1) can or cannot lie on line q.
Examples in Statement 1 can be considered here also [line x = 1 and line x = 2].
Statement 1 and Statement 2 together are Not Sufficient.
So, correct answer is option E.