What you should know, IMHO, to solve this one is that you need to know the coordinates of two points in order to find the equation of a line. So, because of this, either 1 or 2 are insufficient. But if you take them together, then you have the required two points, so you can find k's equation. It will be smth like y = a*x + b. Then you can test to see if the given point is on line k or not, simply by replacing x with 4 and seeing if 4a + b does equal 12.

I'd say C.

In order to find out whether the point (4,12) lie on line K..we shud know the slope of the line...to calculate it we need to know atleast two points on line.....
equation of line: y=mx+b
wher m is the slope of line {m= (y2-y1)/(x2-x1) & b= y intersect}

The slope of point (4,12) shud match with the slope of the line K for it to exist on the same line....

Since, taking together 2 statement wud suffice our req...ans is C

There's not much to add here other than to realize that:

1) once you CAN answer the question, you don't need to go any farther. The more practice tests I take, the better I am getting at realizing when I have proven the DS answer and stopping so as to have more time for the rest of the questions.

And 2) to remember that we don't need to know THAT 4,12 is a point on the line k, we just need to know IF 4.2 is a line on point k. NO is as good an answer as YES is here and I am getting more comfortable with that about DS questions.

This DS questions demonstrates those two points nicely.

-Carrie