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

1

This post received KUDOS

00:00

A

B

C

D

E

Difficulty:

25% (low)

Question Stats:

63% (01:41) correct
36% (01:44) wrong based on 71 sessions

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.

Spring has passed, summer is gone and winter is here. And the song that I meant to sing remains unsung. For I have spent my days stringing and un-stringing my instrument.

Last edited by AbhiJ on 21 May 2012, 00:02, edited 3 times in total.

Re: In the xy-plane, does the line L intersect the graph of y = [#permalink]
19 Jan 2013, 04:13

1

This post received KUDOS

Expert's post

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 [ 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.

Re: In the xy-plane, does the line L intersect the graph of y = [#permalink]
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.

Re: In the xy-plane, does the line L intersect the graph of y = [#permalink]
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.

Re: In the xy-plane, does the line L intersect the graph of y = [#permalink]
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.
_________________

Re: In the xy-plane, does the line L intersect the graph of y = [#permalink]
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 .
_________________

Spring has passed, summer is gone and winter is here. And the song that I meant to sing remains unsung. For I have spent my days stringing and un-stringing my instrument.

Re: In the xy-plane, does the line L intersect the graph of y = [#permalink]
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.

Re: In the XY-Plane does line l intersect the graph of y=x^2? [#permalink]
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....

Re: In the xy-plane, does the line L intersect the graph of y = [#permalink]
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?

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