Possible Mistake On MGMAT CAT Question

[geatkins]

The following question appeared on the very first MGMAT CAT I took last night and I got it wrong.

Does line S intersect line segment QR?

(I didn't know how to copy the picture but line QR has points (1,3) & (2,2))

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

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

I answered D, each statement alone alone is sufficient.

However, I got the question wrong in the CAT with an answer explanation as show below. This answer explanation seems to me, well, "Insufficient." The question of course as whether you can determine if line S intersects line QR. Thus an answer of "yes it does" or "no it doesn't" is "Sufficient", leading to my answer D. It doesn't actually have to intersect, as the answer explanation seems to suggest, at least to me.

I'm scoring in the 640's so I may be missing something here.

What am I missing? Thanks in advance for any comments or ideas.

Glenn Atkins

Explanation:

Lines are said to intersect if they share one or more points. In the graph, line segment QR connects points (1, 3) and (2, 2). The slope of a line is the change in y divided by the change in x, or rise/run. The slope of line segment QR is (3 - 2)/(1 - 2) = 1/-1 = -1.

(1) SUFFICIENT: The equation of line S is given in y = mx + b format, where m is the slope and b is the y-intercept. The slope of line S is therefore -1, the same as the slope of line segment QR. Line S and line segment QR are parallel, so they will not intersect unless line S passes through both Q and R, and thus the entire segment. To determine whether line S passes through QR, plug the coordinates of Q and R into the equation of line S. If they satisfy the equation, then QR lies on line S.

Point Q is (1, 3):
y = -x + 4 = -1 + 4 = 3
Point Q is on line S.

Point R is (2, 2):
y = -x + 4 = -2 + 4 = 2
Point R is on line S.

Line segment QR lies on line S, so they share many points. Therefore, the answer is "yes," Line S intersects line segment QR.

(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.

The correct answer is A.

[tim]

Thus an answer of "yes it does" or "no it doesn't" is "Sufficient".

That is correct. But statement 2 does not yield a definite "yes it does" or "no it doesn't"; the explanation very clearly demonstrates how it could be either yes or no. This means 2 is NOT sufficient..

[geatkins]

Tim,

Interesting. I totally missed, and thus failed to consider, that the line in statement 2 could in fact be on top of the line in the question. I interpreted parallel to mean parallel, but not on top of. Duh! That was really tricky for my simple little mind.

Thanks for answering.

Glenn

[RonPurewal]

Tim,

Interesting. I totally missed, and thus failed to consider, that the line in statement 2 could in fact be on top of the line in the question. I interpreted parallel to mean parallel, but not on top of. Duh! That was really tricky for my simple little mind.

Thanks for answering.

Glenn

hmm, yes, we should probably fix the answer explanation so that it is more technically accurate -- for instance, "either parallel or coincident".

the word "parallel" should not be used in the case of coincident lines; thanks for calling this to our attention.