Lines k and l intersect in the coordinate plane at point (3,

It's a good question. We can solve it by visualizing the situation.

First of all, whenever two lines intersect, the four angles between them make up 360 degrees. Either the lines can be perpendicular in which case all angles are 90 degrees or the lines are not perpendicular in which case two angles are less than 90 and other two are more than 90. So all we have to figure out is whether the lines can be perpendicular (in which case there is no angle greater than 90). In every other case, there will be an angle greater than 90.

(1)Lines k and l have positive y- axis intercepts
The black dotted lines show perpendicular lines. You can move them around as you want keeping the angle constant; there is no way both lines will have positive y intercept.



Also, recall that the product of slopes of two perpendicular lines is -1. If one line has positive slope, the other must have negative slope.
We can say that the lines cannot be perpendicular. Hence, there must be two angles greater than 90. Sufficient.

(2) The distance between the y-axis intercepts of lines k and l is 5
A little trickier. Let's try to figure out whether two perpendicular lines meeting at (3, -2) can have a distance of 5 between their y intercepts. Notice the purple and green lines in the figure above. The distance between the y intercepts is quite large. The distance will be smallest when the two line segments are of equal length.


In the isosceles right triangle shown above, let's try to find x so that we know the minimum value of distance between the y intercepts.

\((1/2)*3*\sqrt{2}x = (1/2)*x*x\) (Area of the triangle using altitude = Area of triangle using two sides)
\(x = 3\sqrt{2}\)

The distance between the y intercepts must be at least \(\sqrt{2}x\) i.e. 6.

Hence we can say the lines cannot be perpendicular. Sufficient.

Answer D