Parallel Lines !!!!

[Saurav]

Question 15 of 37 in CAT-3

Does line S intersect line segment QR?
Information in figure - QR is a line with the end points at Q (1,3) and R (2,2)

(1) The equation of line S is y = -x + 4.

(2) The slope of line S is -1.

The correct answer is Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

The correct answer should be EACH statement ALONE is sufficient.

This is because the line defined in condition 2 is parallel and 2 parallel lines by definition cannot intersect (overlaying of parallel lines in not intersection in geometry) external reference - http://en.wikipedia.org/wiki/Parallel_(geometry)

The solution says that condition

(2) INSUFFICIENT: Line S has the same slope as line segment QR, so they are parallel. They might intersect; for example, if Line S passes through points Q and R. But they might never intersect; for example, if Line S passes above or below line segment QR.

I think the answer to this question should be changed.

[Capthan]

I think the statement 2 is suggesting that line S is laying exectly on the line QR because they have the same slope not above the line QR or under the line QR.

[Saurav]

Capthan,

You are right.

Overlaying lines do not mean intersection (since they are parallel), intersection of two lines must define a single point.
from another point, Overlaying lines = infinite number of intersection points (i am not sure if that can be considered a classical definition of intersection of two lines)

[esledge]

You have a point. I have definitely seen this definition: "In two dimensions, two different lines can either be parallel, meaning they never meet, or may intersect at one and only one point." (From Wikipedia, but I have read this elsewhere, too.) The OG simply says "If two lines that are in the same plane do not intersect, the two lines are parallel." (p.128). That begs the question: Would the OG therefore conclude that S must not intersect QR, because it clearly is parallel (same slope)? That is, if not intersecting means parallel, does parallel mean not intersecting?

I'll forward this to our curriculum director for a decision. I think there is enough terminology ambiguity to warrant a change to something like "Does line S touch line segment QR?" though that sounds hokey to me. Probably a better change is to the line equation itself, perhaps making the statements (1) y = x + 1, and (2) The slope of line S is 1.

[StaceyKoprince]

I have seen mathematical interpretations of "intersect" to mean "cross at one point only" and interpretations in which "intersect" means "cross at one or more points." I'm not sure how the GMAT test writers interpret this definition. We'll see if we can find a definitive answer in the existing commentary (OG, et al). If so, then we go with GMAC's usage interpretation. If not, we'll have to avoid testing this ambiguity unless / until we get a definitive ruling from GMAC.

[Saurav]

Thank you both Emily and Stacey for looking into this. I feel good to be a part of this community. It would be right to see how GMAC interprets the terms here.