[edited]


K passes through the point (1,1) and M passes through the point (1,-1)

Statement 1
Line k and m intersect at (1,-1)

We get the slope of line k , which is parellel to the Y-axis

but we have no clue about the slope of line m
Not sufficient


Statement 2
Line k intersects the x-axis at (1,0)

line k is parellel to y axis .
but this time we have no idea about the slope of line m
Not Sufficient


but combining both the statements also wont tell us aythin about line



Option E

Both statements tell us that line k is parallel to y axis and that it meets m at point (1,-1).
But we don't have any further information on line m.
It may be parallel to x axis (slope 0) and thus be perpendicular to line k
OR
have a negative or positive slope and not be perpendicular to line k.

Hence insufficient (E)

Statement 1 says that K is parallel to Y axis, and intersects with M at (1,-1), so these two lines intersect. But it tells nothing about the slope of M. So insufficient.

Statement 2 also says the same thing but does not tell anything about the slope of M. Insufficient.

Combining 1 and 2 also tells nothing about the slope of M.

So, answer should be E.