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

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Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 07 Oct 2013, 10:04
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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?
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 20 Mar 2014, 04:52
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unceldolan wrote:
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??


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.

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
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 07 Oct 2013, 12:16
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joylive wrote:
Image
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?


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.
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 07 Oct 2013, 12:34
1
joylive wrote:
Image
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?



Hey..
Statement 1:
We find the slope of the line QR=(3-2)/(2-1)=1.
If we hurry, we can conclude that the lines intersect at 90 degree. Hence intersect each other.
But this line can be anywhere in the plane and it may or maynot intersect the line QR.
Hence insufficient.

Statement 2:
Since we have the line we can easily find out if they intersect or not. NO NEED TO CALCULATE.

Hope this helps.

Hit kudos if this helped.
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 07 Oct 2013, 12:54
Quote:
We find the slope of the line QR=(3-2)/(2-1)=1.


The slope of line segment QR is -1, e.g. \((3-2)/(1-2)=-1\) Make sure to keep your inputs to the numerator and denominator the same to be \(y1-y2/x1-x2.\)
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 07 Oct 2013, 20:54
blueseas wrote:
joylive wrote:
Image
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?


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.


Well for parallel lines, isn't m1 = m2, wouldn't this apply to statement 1 ?
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 07 Oct 2013, 21:45
1
joylive wrote:
Image
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?


Statement 1 says the slope is -1. Therefore it will be 45 Deg line and can pass through any where. For instance say it intersects x-axis at +100 then it won't intersect the line segment given. If it psses through +4 at x-axis then it will intersect. So NOT SUFFICIENT.

Statement 2 gives us 1 equation. And since we have coordinates of the line segment we can get 1 equation.

Hence 2 equations, solving we can get x and y points at which they intersect. Or if they don'e intersect.

Hence B is the answer!!

Consider Kudos if its clear. That's a good way to motivate.
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 21 Oct 2013, 16:59
shameekv wrote:
joylive wrote:
Image
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?


Statement 1 says the slope is -1. Therefore it will be 45 Deg line and can pass through any where. For instance say it intersects x-axis at +100 then it won't intersect the line segment given. If it psses through +4 at x-axis then it will intersect. So NOT SUFFICIENT.

Statement 2 gives us 1 equation. And since we have coordinates of the line segment we can get 1 equation.

Hence 2 equations, solving we can get x and y points at which they intersect. Or if they don'e intersect.

Hence B is the answer!!

Consider Kudos if its clear. That's a good way to motivate.


If a line P passes through/overlaps line segment QR does it mean that line P intersects QR at all points on line segment QR??
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 20 Mar 2014, 03:47
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??
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 02 May 2015, 13:10
blueseas wrote:
joylive wrote:
Image
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?


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.



Hi blueseas,

For the stmt 1, you have explained good, but "y = -x + 4 ==>this line will intersect the QR segment at Q(1,3)" must be R(2,2) because when we solve the equation,
X=0---> y=4 and when Y=0--->x=4. Therefore the equation comes like, Line y=-x+4 has (4,4) point.. from origin (0,0), which will start from (0,0) to (4,4). So y = -x + 4 intersects at R(2,2) and not Q(1,3).. Please correct me if I am wrong.. Also could someone solve the 2nd stmt for more clarification for 2 lines intersect finding.. Theory or formula could do fine...
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 02 Jul 2015, 05:24
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 ??
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 02 Jul 2015, 05:45
vipulgoel wrote:
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 ??


Technically, yes.
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 21 Dec 2017, 11:03
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

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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 25 May 2018, 09:11
EMPOWERgmatRichC wrote:
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:

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if PQ segment and the line have same slope, then they are parallel to each other.so how can they ever intersect?
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Re: Does line P (not pictured) intersect line segment QR in the  [#permalink]

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New post 25 May 2018, 10:39
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).

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Re: Does line P (not pictured) intersect line segment QR in the &nbs [#permalink] 25 May 2018, 10:39
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