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In the xy-plane, does the line L intersect the graph of y =

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In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 20 May 2012, 07:56
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In the xy-plane, does the line L intersect the graph of y = x^2

(1) Line L passes through (4, -8)
(2) Line L passes through (-4, 16)

OA after some discussion.

My doubt is there is a line passing through (-4, 16) that will be tangent to the curve at this point. Can we still say that this line intersects the curve ? I was thinking this line will touch the curve and not intersect it.
[Reveal] Spoiler: OA

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Last edited by AbhiJ on 21 May 2012, 00:02, edited 3 times in total.
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Re: In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 19 Jan 2013, 04:13
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fozzzy wrote:
Tough question! Does anyone have a detailed solution for this one


In the XY-Plane does line l intersect the graph of y=x^2?

(1) Line l passes through the point (4, -8). Consider the diagram below:
Attachment:
Intersection.png
Intersection.png [ 9.48 KiB | Viewed 1655 times ]
As you can see line passing through (4, -8) may or may not intersect with the graph of y=x^2. Not sufficient.

(2) Line l passes through the point (-4, 16). Since (-4)^2=16, then point (-4, 16) is ON the graph of y=x^2, thus line passing through this point intersects the graph of y=x^2. Sufficient.

Answer: B.

Hope it's clear.
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Re: In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 20 May 2012, 08:32
1) This is clearly insufficient. It is possible that the line might intersect the curve at 4,16 ( if it has slope 0, like x=4), or might not intersect at all, like line y=-8.

2) This is sufficient as the line satisfies the equation of the curve y=x^2, 16=(-4)^2, therefore the line and curve intersect at this point.

Answer should be B.
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Re: In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 29 Jun 2012, 06:54
Hi Bunuel/Karishma,

I was able to solve this question by passing values in the equation y=x^2 and have found the correct answer. For reviewing the question, I googled it and ve found that Gmat instructors are rating this question -HARD.
Could you please give me an idea what makes this question Hard. I'm bit skeptical about my approach now..

Thanks
H

AbhiJ wrote:
In the xy-plane, does the line L intersect the graph of y = x^2

(1) Line L passes through (4, -8)
(2) Line L passes through (-4, 16)

OA after some discussion.

My doubt is there is a line passing through (-4, 16) that will be tangent to the curve at this point. Can we still say that this line intersects the curve ? I was thinking this line will touch the curve and not intersect it.

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Re: In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 29 Jun 2012, 07:00
Expert's post
imhimanshu wrote:
Hi Bunuel/Karishma,

I was able to solve this question by passing values in the equation y=x^2 and have found the correct answer. For reviewing the question, I googled it and ve found that Gmat instructors are rating this question -HARD.
Could you please give me an idea what makes this question Hard. I'm bit skeptical about my approach now..

Thanks
H

AbhiJ wrote:
In the xy-plane, does the line L intersect the graph of y = x^2

(1) Line L passes through (4, -8)
(2) Line L passes through (-4, 16)

OA after some discussion.

My doubt is there is a line passing through (-4, 16) that will be tangent to the curve at this point. Can we still say that this line intersects the curve ? I was thinking this line will touch the curve and not intersect it.


Personally I wouldn't rate this question as hard. I think its difficulty level is ~600, not more.
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Re: In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 29 Jun 2012, 10:55
imhimanshu wrote:
Hi Bunuel/Karishma,

I was able to solve this question by passing values in the equation y=x^2 and have found the correct answer. For reviewing the question, I googled it and ve found that Gmat instructors are rating this question -HARD.
Could you please give me an idea what makes this question Hard. I'm bit skeptical about my approach now..

Thanks
H

AbhiJ wrote:
In the xy-plane, does the line L intersect the graph of y = x^2

(1) Line L passes through (4, -8)
(2) Line L passes through (-4, 16)

OA after some discussion.

My doubt is there is a line passing through (-4, 16) that will be tangent to the curve at this point. Can we still say that this line intersects the curve ? I was thinking this line will touch the curve and not intersect it.


GMAC rates this Q as hard , if you ask me there is a reason for it.

There is a line passing through (-4, 16) that will be tangent to the curve at (-4, 16). Can you say that a tangent intersects a curve. The literature says the tangent touches a curve, not sure if touch and intersect are the same thing. Intersect means dividing in sects/sections. However the tangent lies totally outside the curve.

This fact would make B insufficient as there is one line the tangent that does not intersect the curve. Hence the answer would be C and not B.

--------------------------------------------------------------------------------------

If however you take the mathematical definition that an equation of line and curve can be solved for one or more points then the line intersects the curve, then B will be sufficient. That's how i was able to digest the solution :).
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Re: In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 21 Nov 2012, 10:50
AbhiJ wrote:
imhimanshu wrote:
Hi Bunuel/Karishma,

I was able to solve this question by passing values in the equation y=x^2 and have found the correct answer. For reviewing the question, I googled it and ve found that Gmat instructors are rating this question -HARD.
Could you please give me an idea what makes this question Hard. I'm bit skeptical about my approach now..

Thanks
H

AbhiJ wrote:
In the xy-plane, does the line L intersect the graph of y = x^2

(1) Line L passes through (4, -8)
(2) Line L passes through (-4, 16)

OA after some discussion.

My doubt is there is a line passing through (-4, 16) that will be tangent to the curve at this point. Can we still say that this line intersects the curve ? I was thinking this line will touch the curve and not intersect it.


GMAC rates this Q as hard , if you ask me there is a reason for it.

There is a line passing through (-4, 16) that will be tangent to the curve at (-4, 16). Can you say that a tangent intersects a curve. The literature says the tangent touches a curve, not sure if touch and intersect are the same thing. Intersect means dividing in sects/sections. However the tangent lies totally outside the curve.

This fact would make B insufficient as there is one line the tangent that does not intersect the curve. Hence the answer would be C and not B.

--------------------------------------------------------------------------------------

If however you take the mathematical definition that an equation of line and curve can be solved for one or more points then the line intersects the curve, then B will be sufficient. That's how i was able to digest the solution :).



It's definitely rated as a hard question.

Touching and intersecting mean the same thing . This is because the lines share a common point.

Hence, you arrive at B

Thanks,
Ankit
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In the XY-Plane does line l intersect the graph of y=x^2? [#permalink] New post 15 Dec 2012, 14:06
In the XY-Plane does line l intersect the graph of y=x^2?

(1) Line l passes through the point (4,-8)
(2) Line l passes through the point (-4.16)

Last edited by Bunuel on 16 Dec 2012, 07:38, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In the XY-Plane does line l intersect the graph of y=x^2? [#permalink] New post 15 Dec 2012, 15:30
mun23 wrote:
In the XY-Plane does line l intersect the graph of y=x^2?

(a)Line l passes through the point (4,-8)
(b)Line l passes through the point (-4.16)

Need details explanation
If you find this post helpful plz give+1 kudos


y=x^2 is a parabola with vertex at (0,0) and upward......

(a) Line passes through (4,-8); if line is parallel to X-axis it can never intersect the parabola.... if line is parallel to Y-axis it will... Not Sufficient
(b) Line passes through (-4,16); observe that this point is on y=x^2 which means line is intersecting parabola at the point.... It may or maynot intersect y=x^2 at some other point, we don't bother about it.... because question asks for if the line is intersecting y=x^2 or not... so just a yes or no question.... in this case it is intersecting the graph... so sufficient....

Answer is B
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Re: In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 19 Jan 2013, 00:41
Tough question! Does anyone have a detailed solution for this one
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Re: In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 23 Apr 2014, 20:32
Hi Gurus,

My question may be absurd but please help me understand the concept here. When I see y=x^2 i do not see it as an Upright parabola but a parabola drawn towards positive x axis . Say y=-3 then x^2 = 9 so (-3,9) is on the parabola, similarly (-2,4),(-1,1),(0,0),(1,1) and (2.4) all should form the parabola with function y=X^2.

Now if line l passes through (-4,16)- statement B, i see it as x co-ordinate as -4 and y co-ordinate as 16 then this point does not lie on the parabola. Can anyone please explain where am I at fault?

Thanks in advance.

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Re: In the xy-plane, does the line L intersect the graph of y = [#permalink] New post 24 Apr 2014, 01:43
Expert's post
amariappan wrote:
Hi Gurus,

My question may be absurd but please help me understand the concept here. When I see y=x^2 i do not see it as an Upright parabola but a parabola drawn towards positive x axis . Say y=-3 then x^2 = 9 so (-3,9) is on the parabola, similarly (-2,4),(-1,1),(0,0),(1,1) and (2.4) all should form the parabola with function y=X^2.

Now if line l passes through (-4,16)- statement B, i see it as x co-ordinate as -4 and y co-ordinate as 16 then this point does not lie on the parabola. Can anyone please explain where am I at fault?

Thanks in advance.

Arun


I think you should brush-up fundamental on coordinate geometry:
Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62


As for your question, check the graph of y=x^2 and the point (-4, 16) on it:
Attachment:
Untitled.png
Untitled.png [ 11.71 KiB | Viewed 3 times ]
To check whether (-4, 16) is on y=x^2, substitute x=-4 there and check whether y comes out to be 16: (-4)^2=16, so (-4, 16) is on y=x^2.

Hope it helps.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In the xy-plane, does the line L intersect the graph of y =   [#permalink] 24 Apr 2014, 01:43
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