Two lines intersect...

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Svedankae: Master | Next Rank: 500 Posts; Posts: 101; Joined: Tue Apr 07, 2009 12:30 am; Thanked: 2 times; GMAT Score:750

Two lines intersect...

by Svedankae » Sun Sep 20, 2009 8:32 am

Hello,

just a quick question: In a MGMAT CAT i came across this question asking whether some line S intersects some segment QR. (see picture).

In the solution they say that if a segment lies on a line, it can be said that the line intersects the segment. i am very astonished to read this, i think its just plain incorrect. I always thought that two lines or a line and a segment only intersect in one point, and in one point only. What do you guys think?

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Source: Beat The GMAT — Data Sufficiency | Sun Sep 20, 2009 8:32 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: Two lines intersect...

by Brent@GMATPrepNow » Mon Sep 21, 2009 8:36 am

Svedankae wrote:Hello,

just a quick question: In a MGMAT CAT i came across this question asking whether some line S intersects some segment QR. (see picture).

In the solution they say that if a segment lies on a line, it can be said that the line intersects the segment. i am very astonished to read this, i think its just plain incorrect. I always thought that two lines or a line and a segment only intersect in one point, and in one point only. What do you guys think?

This really comes down to GMAC's definition of "intersect." I've tried looking for the definition in the Official Guide, but can't find it.

To give some insight, there is one official GMAT question that asks:
Which of the following lists the number of points at which a circle can intersect a triangle?
A. 2&6 only
B. 2,4&6 only
C. 1,2,3&6 only
D. 1,2,3,4&6 only
E. 1,2,3,4,5&6

The answer to this question might help us get an idea of GMAC's definition of "intersect."
Many of my students see an intersection as a line passing through something (much like a traffic intersection). If this is your definition, then a line that is tangent to a circle at one point would not be seen as intersecting the circle, since the line does not pass through the circle.
The official answer to the blue question above is E, so we can see that the definition of intersect in this example suggests that for a line to intersect something, that line need only share one point (or more) with that something.

If this is the case, then the line in the original question would seem to share at least one point with the line segment, in which case it would be intersecting.

That's my take on it.

Brent Hanneson - Creator of GMATPrepNow.com