Alchemist87 wrote:
Dear Mike/ experts,
Considering stm 1 and 2 together: what if R is parallel to Y axis, hence its slope is infinity and it has no Y intercept. S can be any line with positive Y intercept. We can have a scenario where both these lines intersect such that both its coordinates are negative (stm 1) and considering that infinity is more than the slope of line S (say having positive slope of 50) , it also adheres to stm 2. But here intercept of R (nil) is not more than intercept of S (some positive value).
Dear
Alchemist87,
I'm happy to respond.
First, I will say that this is a very creative and out-of-the-box observation. This creativity will serve you well in your career.
In this particular problem, though, I think that case is eliminated by the question. Here's the text of the question again:
Lines r and s lie in the xy-plane. Is the y-intercept of line r less than the y-intercept of line s ?
(1) At the intersection point of r and s, the x-coordinate and y-coordinate are both negative.
(2) The slope of line r is greater than the slope of line s.If the question is asking whether one quantity is less than another quantity. It would be devious and tricky in a way that the GMAT simply does not do if one of the quantities about which it was asking in that context simply did not exist. The fact that the GMAT asks about the two y-intercepts really implies, among other things, that they both exist.
Now, a vertical line R might be consistent with Statement #1 by itself, by this statement by itself is not sufficient anyway.
Once we get to statement #2, we get another prohibition: although stated verbally, the statement (slope R) < (slope S) is a well-defined mathematical statement. We can only make well-defined mathematical statements with numbers that exist on the number line. Metaphorically, we can say that infinity is "bigger" than any given number, but we can't actually state that fact as a well-defined mathematical statement. (There are many different
kinds of infinity, but that's mathematics that is well beyond the GMAT!) In practice, any value that becomes infinite, such as 1/0, is called "undefined," precisely because it departs from the region for which we can make well-defined statements.
Therefore, both the prompt and statement #2 make a vertical line impossible in this problem.
I want to emphasize, though, what you asked was truly a brilliant question, my friend. Let me know if you have any more questions.
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)