Does line P (not pictured) intersect line segment QR in the

Question

https://jasper.kaptest.com/content/media/66/212266.12.MG0606_img01.gif 
Does line P (not pictured) intersect line segment QR in the coordinate plane shown above?

(1) The slope of line P is –1.

(2) The equation of line P is y = –x + 4.

Me personally thinks the answer should be D, but OA differs, as usual. Can someone help please?

Bunuel · Accepted Answer

Technically intersect means share one or more points in common. So, if two lines overlap they do intersect. Thus from (1) if line P contains line segment QR then they intersect but if line P is parallel to line segment QR, then they do not intersect, which means that the first statement is not sufficient.

Bunuel , having what you mentioned above ,Can we say that line laying on x axis , intersects with x axis ??

Having said that, I must add that GMAT would never test you on such technicalities, so the question is poor and one can ignore it and move on.

Hope it help.s

blueseas · Answer

D cannot be answer.
statement 1 says slope is -1. so this line can pass from anywhere only restriction is that it should have a slope of -1.
let take 2 example. 
y = -x + 4 ==>this line will intersect the QR segment at Q(1,3)
y = -x-8 ===>this is not going to intersect the line segment QR.

HENCE STATEMENT 1 IS INSUFFICIENT.

STATEMENT 2 SAYS:
this gives the fixed line ....so you will get a definite answer either YES OR NO.
no need to calculate.

hence its B

HOPE IT HELPS.

unceldolan · Answer

Guys, I don't get it, for me it's D too. IF a m1=m2, the lines are parallel so NEVER INTERSECT, only overlap?? Or do I get the wording wrong??

vipulgoel · Answer

Technically intersect means share one or more points in common. So, if two lines overlap they do intersect. Thus from (1) if line P contains line segment QR then they intersect but if line P is parallel to line segment QR, then they do not intersect, which means that the first statement is not sufficient.

Bunuel , having what you mentioned above ,Can we say that line laying on x axis , intersects with x axis ??

Bunuel , having what you mentioned above ,Can we say that line laying on x axis , intersects with x axis ??

Bunuel · Answer

Technically, yes.

EMPOWERgmatRichC · Answer

Hi All,

This is a great 'concept' question; if you recognize the concepts involved, then you don't actually have to do any math to get to the correct answer.

We're asked if a line P intersects with the line segment QR. This is a YES/NO question.

1) The slope of line P is -1.

This Fact tells us the slops of line P, but it doesn't tell us exactly where line P is located. Thus, it might intersect the line segment or not. 
Fact 1 is INSUFFICIENT

(2) The equation of line P is y = -x + 4.

This Fact gives us the exact equation for line P, so we COULD graph it... and once we did, we'd know definitively whether line P intersected with the line segment or not (and there would be just one answer to the given question). 
Fact 2 is SUFFICIENT

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

JAIN09 · Answer

if PQ segment and the line have same slope, then they are parallel to each other.so how can they ever intersect?

EMPOWERgmatRichC · Answer

Hi JAIN09,

From your message, I assume that you're questioning the definition of "intersect." A typical example would be two lines that are perpendicular to each other; they WILL intersect at exactly ONE point. In this question though, with the line segment that's in the drawing - and the equation that we're given in Fact 2 - there are actually MULTIPLE points of intersection since the line falls exactly "on top" of the line segment. In that way, the two lines DO intersect (just not in the way that you're used to thinking about the concept). This is ultimately why Fact 2 is sufficient (the line and the line segment DO share several common intersect points).

GMAT assassins aren't born, they're made, 
Rich

Rashed12 · Answer

Hallo,

To me, the answer is D. But unfortunately I did not understand why the answer is B, though I have read the above explanations.
Would anyone draw graph to make clear understanding why A is not correct?

EMPOWERgmatRichC · Answer

Hi Rashed12,

I think that you can properly prove that Fact 1 is insufficient if you are comfortable drawing a couple working through a few steps:

1) Draw a graph and line segment QR (the pictured segment).
2) Draw ANY line with a slope of -1. You can put that line wherever you want. Does your line cross the given line segment? Most lines you could create would not (and it's likely that the first line you would draw would not intersect the segment).
3) Can you draw a different line (also with a slope of -1) that would intersect line segment QR? Where would you have to put it?

Thus, the line described in Fact 1 might intersect line segment QR, but it might not. 
Fact 1 is INSUFFICIENT

GMAT assassins aren't born, they're made, 
Rich

puneetfitness · Answer

Posted from my mobile device     Posted from my mobile device

EMPOWERgmatRichC · Answer

Hi puneetfitness, We're asked if a line P intersects with the line segment QR (which appears at a specific point on the graph and has a slope of -1). This is a YES/NO question. 1) The slope of line P is -1. This Fact tells us the slops of line P, but it doesn't tell us exactly where line P is located. Thus, it might intersect the line segment (by lying right "on top" of segment QR) or not. Fact 1 is INSUFFICIENT GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com

aronbhati · Answer

Hi Bunuel,

Please show with graph that equation Y=-x+4 intersect or not to the mentioned line in question.

you are saying it is intersecting then why slope of both lines are same that is -1

Does line P (not pictured) intersect line segment QR in the

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