Good DS question - Cogeo II

austin wrote:When we say intercept of 3, it means distance is 3...

Intercepts are *not* distances, they are coordinates. They can be negative, and they can be positive. If the y-intercept of a line is b, then the distance from the y-intercept to the origin will always be equal to |b|, and not necessarily to b (b can be negative). If a line has a y-intercept of 3, that guarantees that the point (0,3) is on the line, and unless the line is vertical, that also guarantees that the point (0, -3) is *not* on the line.

sanju09 wrote:For statement (1) in particular:

In order to include the possibility that both the intercepts could be equal to 0; the phrase "x-intercept is twice the y intercept" would have been written as "x-intercept is (some) k times the y intercept, where k is not 0", instead of fixing a value for k, so I still believe that if the two statements were not contradicting here, this could have been a possible GMAT question with A as the answer.

I don't think you'll see a phrase like the one in the question on a real GMAT anyway (I don't think I've ever seen a question that uses 'twice' to mean 'two times'). That said, you can certainly see an equation like:

x = 2y

and you can't dismiss the possibility that x = y = 0, of course. Taking the statement literally, the intercepts could certainly both be zero; that's an entirely logical conclusion from the statement, as it is worded. If the GMAT wants to exclude that possibility, this will be made perfectly clear in the wording of the question; otherwise the question would not be fair.

I agree that it is a more interesting question, and a more GMAT-like question, if somehow the question conveys that the x- and y-intercepts are not at the origin. Then, of course, one of the statements needs to be changed so that they are not contradictory.