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line intersection??

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by ch0719 » Sun Jan 04, 2009 10:26 pm
This is a question from MGMAT CAT online

My answer was D, but answer provided by MGMAT is A, and here is the explanation:

[spoiler]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. [/spoiler]


So here's my question: if Line S passes through points Q and R does it mean they intersect? Because imo for S to intersect with the line QR, line S must be able to devide line QR into two parts, thus if the slope of line S is same with the slope of QR then it means they will never intersect. I also remember that the theory goes two parallel lines never intersect.

Any other opinions? :shock:
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by cramya » Sun Jan 04, 2009 10:57 pm
This one puzzles me also.

Stmt I and II pretty much gives the same info.

I would have choose D) also.

I am unable to understand how parallel lines will ever intersect. May be we are missing something.

The reason given for 1 could apply for 2 also since the slopes are being considered.
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by scoobydooby » Sun Jan 04, 2009 11:01 pm
statement 1: says the lines are distinct and parallel.
statement 2: lines have same slope, we do not know if lines are distinct

have a confusion: are coincident lines said to intersect? i thought intersection meant cutting the line at a distinct point.
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by logitech » Mon Jan 05, 2009 2:43 am
The axiom in Euclidian Geometry is that parallel lines never intersect.

The axiom in non-Euclidian Geometry is that parallel lines intersect at infinity.

Statement 1) gives us the same line in question stem. So they overlap, is overlapping an intersection ? SURE ( You can also hear from a mathematician NO! )

Statement 2) IT might or MIGHT NOT - Slopes are the same but we don't know any other information about the line.
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by bsandhyav » Mon Jan 05, 2009 3:46 am
cramya wrote:This one puzzles me also.

Stmt I and II pretty much gives the same info.

I would have choose D) also.

I am unable to understand how parallel lines will ever intersect. May be we are missing something.

The reason given for 1 could apply for 2 also since the slopes are being considered.


Def'n of intersecting lines: If a line has 1 or more points in common with another line the lines are said to be intersecting lines.


Coincident lines have all points in common ( i.e one or more than one). Hence they are considered to be intersecting lines.


St 1 : Since this statement gives the equation of the line S we can verify that the points on the segment coincide with that of line S. Hence the answer is YES. They are coincident lines


St2: This statement just mentions that the two slopes are the same(i.e -1).
This implies that the lines are either parllel (ie. non intersecting) or co-incident (which according to the def'n above are intersecting).
Hence we cannot say anything surely.

So St 1 alone is sufficient and st 2 is not IMO A

Hope this could make it clearer
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by cramya » Mon Jan 05, 2009 8:51 pm
Thanks Sandhya!
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by rajataga » Sat Jan 10, 2009 5:55 am
ch017, wat you were talking about is called 'bisection' that is dividing the line into half.

Intersection is just a common point/s between 2 figures.
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by GMAT680 » Fri Mar 12, 2010 4:20 pm
I think the explanation for statement 2 need to be. The lines are parallel and will never intersect. On the other hand, the given slope can be a slope of the given line. Hence, it overlaps (intersects).

That is the only justification to dispute choice. However, it disputes the golden rule of parallel lines will never cross each other.
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by girish3131 » Sat Mar 13, 2010 12:13 am
Thanks for posting this ques....

a new maths concept learned after a long time......

GREAT DUDE....!!! keep posting such concept twisting ques.... Thanks once again....!!!
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by sarthak » Tue Mar 16, 2010 2:32 am
New concept ..... hmmm interesting ... guys pls keep on posting such questions
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by sumanr84 » Sun Jul 18, 2010 9:38 am
Today I got this question in MGMAT CAT. Quite tricky, has anyone seen anything like that ever on GMAT ?

Does anyone knows how GMAT considers below defn..??

Def'n of intersecting lines: If a line has 1 or more points in common with another line the lines are said to be intersecting lines.


Coincident lines have all points in common ( i.e one or more than one). Hence they are considered to be intersecting lines.
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by kvcpk » Sun Jul 18, 2010 9:52 am
sumanr84 wrote:Today I got this question in MGMAT CAT. Quite tricky, has anyone seen anything like that ever on GMAT ?

Does anyone knows how GMAT considers below defn..??

Def'n of intersecting lines: If a line has 1 or more points in common with another line the lines are said to be intersecting lines.


Coincident lines have all points in common ( i.e one or more than one). Hence they are considered to be intersecting lines.
Very tricky indeed. I have no idea about how GMAT treats those definitions. But I believe the idea of the problem is correct.

Maths definition only says that two lines are said to be parallel when they are slopes are equal. This problem exploits that definition by making both the lines same. Need to give credit to the designer of this problem.
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