arora007 wrote:If, on a co-ordinate plane point A has the co-ordinates (-3,4) how fare is point A from point E ?

a) point E is on the y axis 4 units from the origin.

b) If point A were taken twice as far from point E, it would be the same distance from point E as point C is at co-ordinates(0,-2)

From Statement 1, there are two possible locations for point E, at (0,4) and at (0,-4), and since the distance from A to E will be different in each case, Statement 1 is not sufficient.

Statement 2 is also not sufficient; it just tells us that the distance AE is half of the distance CE. We might imagine connecting points A and C. There will be a point on that line which is twice as far from C as from A (the point is at (-2, 2)). This will give us the closest possible point to A; the distance AE is then sqrt(5). But, as the first statement might help us to see, Point E might be at (0,4), in which case the distance AE is 3, among other possibilities.

Combined, the only way both statements can be true is if E is at (0,4), so the answer is C.

ankurmit wrote:

Cordinates of point C are given as (0,-2) and this point will lie on Y-axis only .....please consider this

Yes, the coordinates of point C are given, as are the coordinates of point A. The coordinates of point E, however, are not given, and since we are measuring the distances AE and CE, we need some information about the location of E.

I think it's quite easy to misinterpret Statement 2. Statement 2 does *not* tell you that the length of AC is twice the length of AE. If it told you that, it would certainly be sufficient, since we could find the length of AC using the given coordinates.