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mgmat 6

by resilient » Mon May 26, 2008 12:20 pm
Does line S intersect line segment QR? Point Q is (1,3) and R (2,2)

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

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


statement 1 gives gives line that runs right through it and so it technically cant intersect.

statement two doesnt give the y coordinate to start from so insufficient. How is a sufficient.

I think I am missing a point on intersection. Just because the line runs through it doesnt mean it intersect. statement 1 hinges on this.


qa is a
Last edited by resilient on Mon May 26, 2008 3:38 pm, edited 1 time in total.
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by chidcguy » Mon May 26, 2008 2:13 pm
I am not sure how it is A either

(2) Slope of S is -1, Slope of line formed by points Q (1,3) and R (2,2) is also -1 (2-3)/(2-1) = -1

The line S and Line formed by Q and R are parallel because they have equal slopes. Does parallel lines intersect? No? Isn't that sufficient? Am I missing something?

(1) With A, the line S is Y=-X+4. We can also say that the slope of the line is -1 and slope of line segment formed by QR is also -1. Both of them parallel. So they don't intersect. Going a step ahead and if we see what the line formed by QR is

Y=MX+B; Y= -X+B; Substitute (1,3) 3=-1+B and B=4;

So the line S is nothing but Y=-X+4. A line segment cannot intersect itself. So we have sufficiency.

The answer appears D to me. But I could be missing something
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by netigen » Mon May 26, 2008 8:15 pm
MGMAT provides detailed explanation. Whats the explanation in this case?
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explanation

by resilient » Tue May 27, 2008 5:18 am
this is the explanation but im still not convinced.

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.
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by akshatsingh » Wed May 28, 2008 9:13 pm
I agree with mgmat solution.

2 parallel lines (i.e. same slope) do not intersect.

but here the questuin and the option A talk about the same line.
this is exactly what the quesion wante dus to find out, that these lines are not merely parallel(if we think parallel we choose the wrong answer!!) they are the same lines..
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by netigen » Wed May 28, 2008 10:36 pm
In my opinion, the reasoning is NOT correct:

According to MGMAT

(A) Sufficient because the line S and the segment QR have the same line equation so they intersect at multiple points.

(B) Insufficient as we only know the slope which tells us that S is parallel to QR which mean it can be the same line as QR also hence it may intersect or it may not.

BUT the definition of intersecting lines is that the two lines should meet in one and only one point.

Hence, both the options hold good in this case. I am not sure which Maths dictionary MGMAT is referring to :)

https://www.math.com/school/glossary/def ... lines.html
https://www.hbschool.com/glossary/math2/ ... ines5.html

When lines meet at more than one point, they are said to be co-linear and not intersecting.
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hmm

by resilient » Thu May 29, 2008 5:16 am
I think we need to look at the meaning of the word intersection. However, I do not know if my definition that i find from websters dictionary is same as their definition.
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by chidcguy » Thu May 29, 2008 5:03 pm
How in the world can two parallel lines intersect? This is what https://en.wikipedia.org/wiki/Parallel_( ... )wikipedia says

parallel: they do not intersect in the plane, but do in the limit to infinity

It looks like thats what MGMAT is getting after about two parallel lines.
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hmm

by resilient » Thu May 29, 2008 6:55 pm
I will try to get some mgmat people to talk about this. Makes no sense to me.
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by Stacey Koprince » Sun Jun 15, 2008 9:51 pm
Yes, two parallel lines do not intersect. But the "two" lines described are not parallel - we're only talking about one line. Parallel applies to two lines that share a slope AND are not the same line.

AN intersection refers to one spot where two lines (or other shapes) cross. But you can have more than one intersection for two shapes. Eg, a parabola and a line can intersect at two points.

When you label a situation an Intersecting Line, then yes, those two lines cross at only one point (as opposed to Collinear Lines). But we were not asked whether these two lines represent the definition of an Intersecting Line. The plain word "intersect" just means to cross, or share a point. Is it the case that the "two" lines discussed here share a point? Yes, they do. (All of them, in fact!)

When you say that two lines are collinear, what you are saying is that they intersect at ALL points, not just one. Collinear is a special category, or subset, of the broader case: intersection.
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thank you

by resilient » Mon Jun 16, 2008 4:56 am
There is a huge way to grab many points on the gmat. Many scores make or break according to test takers ability to learn and hold closely to every single detail in the question stem. Thank you Stacy!
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by Stuart@KaplanGMAT » Mon Jun 16, 2008 10:27 am
Everyone is missing an important point: this whole discussion is irrelevant to answering this particular question. No matter which definition you accept, (1) is still sufficient.

If you argue that colinear lines do NOT intersect, then (1) gives you a definite "no": sufficient.

If you argue that colinear lines DO intersect, then (1) gives you a definite "yes: sufficient.

Remember, in DS we don't care what the answer is, what we care about is getting a definite answer to the question.

Here's what our thought process should be on this question:

(1) hey, the equation of line S. If I have the equation, I could graph it out, and I can certainly graph line segment QR. With a full graph, I can definitely determine if the lines intersect: sufficient.

When reviewing questions, it's always nice to see if you understand the underlying concepts and can do the math. However, remember that a lot of high level DS questions are designed to be very time consuming to actually solve (and that the same question would NOT appear in problem solving, precisely because it's too time consuming). What you're really being testing on is your understanding of how DS works and how to apply general math concepts.
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by Ian Stewart » Mon Jun 16, 2008 5:11 pm
Stuart Kovinsky wrote:Everyone is missing an important point:
The most important point, from my view, is that this isn't a real GMAT question. Most of what has been discussed above is irrelevant if you're preparing for the GMAT:

-the GMAT does not test whether you understand obscure technicalities in mathematical definitions;

-if a DS question asks a yes/no question, the answer will always be 'yes' if you have enough information to give an answer. Some test prep books teach that there is a 'trap' on the GMAT, where you may have 'enough information' to answer a yes/no question, but the answer is 'no'. This is test prep book nonsense; this never happens on the current GMAT.

edit: I should add: everything Stuart says above is certainly true, and if you understand the logic in his post, that's the most valuable thing to take from this thread- that's what will help you answer many co-ordinate geometry questions on the GMAT. My issue is with the original question- it is not a real GMAT question- it's not written like a real GMAT question- and because of this it could prove misleading to test takers.
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by Stacey Koprince » Mon Jun 16, 2008 6:17 pm
if a DS question asks a yes/no question, the answer will always be 'yes' if you have enough information to give an answer.
FYI - that used to be true, but GMAT Focus includes questions in which "no" is a definitive answer to a DS yes/no question. Guess they decided to make our lives more complicated... :)
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by Ian Stewart » Mon Jun 16, 2008 6:26 pm
Stacey Koprince wrote:
if a DS question asks a yes/no question, the answer will always be 'yes' if you have enough information to give an answer.
FYI - that used to be true, but GMAT Focus includes questions in which "no" is a definitive answer to a DS yes/no question. Guess they decided to make our lives more complicated... :)
I'd be interested to see those questions. I'd read from official sources that it was now policy to only ask yes/no questions if the answer was yes when the information proved sufficient. Perhaps that's changed (or perhaps GMAT Focus is recycling old GMAT questions!). I've yet to see such a question on GMAT Focus, but of course I haven't completed all of them.
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