Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Circle C and line k lie in the xy plane [#permalink]
24 Aug 2009, 20:29

5

This post received KUDOS

I am getting answer E.

Obviously each statement alone is not sufficient.

Combined analysis: y=-1/10x+a

Finding x intercept: 0=-1/10x+a x=10a

So two points on the line are (10a,0) and (0,a)

from statement 1, it follows that a>1. Assume that a=1, then the points on a line are (10,0) and (0,1). This line with a=1 intercepts the circle at 2 points. Since it intercepts the circle at 2 points, there must be other lines with a>1 that still intercept the circle. Howerver, as value of a increases, a line shifts to the right and up...eventually it will be tangent to the circle and then outside the circle...hard to explain without graph... Since we do not know the value of a, three options possible for a>1: 1) the line intercepts the circle at 2 points 2) the line is tangent to the circle 3) the line is outside the circle. Since we do not know the exact value for a, we can't determine if the line intercepts the circle. I would say both statement are not sufficient - answer E

Re: Circle C and line k lie in the xy plane [#permalink]
24 Aug 2009, 23:03

I too get E, of course without any calculations, just by imagination.

Line with a certain slope can be drawn anywhere in the plane. So it may or may not intersect the circle with radius 1 centered at origin. Only if we had a specific x-intercept we could have concluded that the line intersects the circle or not. Here the x-intercept can be 1,2,3... which has a higher probability to intersect the circle or even 200 which will not intersect the circle.

Re: Circle C and line k lie in the xy plane [#permalink]
25 Aug 2009, 08:44

Economist wrote:

I too get E, of course without any calculations, just by imagination.

Line with a certain slope can be drawn anywhere in the plane. So it may or may not intersect the circle with radius 1 centered at origin. Only if we had a specific x-intercept we could have concluded that the line intersects the circle or not. Here the x-intercept can be 1,2,3... which has a higher probability to intersect the circle or even 200 which will not intersect the circle.

So E for me. OA?

But you first have to make sure that the line with the y intercep set as a limit (in this case a=1) is not a tangent line or does not lie entirely outside the circle. If you are given \(a=X_1\) and the line with this y intercept is tangent to the circle, then: if \(a=x_1<0\), any line with a parameter \(a<x_1\) will be outside the circle if a=X_1>0, any line with a parameter a>x_1 will be outside the circle. You do not have necessarily to know the exact value of the intercepts but in this case the answer is E because a line with the y intercept = 1 crosses the circle in 2 points. Hence for any value of y intercept >1, a line may cross the circle at 2 point, be tangent or lie outside the circle.

Re: Circle C and line k lie in the xy plane [#permalink]
25 Aug 2009, 09:24

sbasha wrote:

Circle C and line k lie in the xy plane. If center of C lie on origin and has radius 1, does line k intersect circle C ?

a. the x intercept of line k is greater than 1. b. the slope of the line is -1/10.

each alone is not suff

wcs assume x intercept is 1 ( 1,0) is the point

y = -1/10x+b , put x = 1,y = 0 thus b = 1/10 thus k intersect the circle. and by using values for x intercept >1 we can get lines that doesnt intersect...hence E

Re: Circle C and line k lie in the xy plane [#permalink]
03 Nov 2009, 02:16

I got the correct answer but am not too sure.. the slope is given at -1/10..what does this say?That the slope is -ive so passes through quad 2 and 4...

but what about the inclination?if its almost parallel to the x-axis it may intersect the circle..not so if the line is almost parallel to y axis..

Basically does the figure of 1/10 tell us anything?What if it was given -5?Would the answer be diff.?

Would like to get the answer without calculations:)Please help. _________________

Re: Circle C and line k lie in the xy plane [#permalink]
07 Nov 2009, 17:38

LenaA wrote:

I am getting answer E.

Obviously each statement alone is not sufficient.

Combined analysis: y=-1/10x+a

Finding x intercept: 0=-1/10x+a x=10a

So two points on the line are (10a,0) and (0,a)

from statement 1, it follows that a>1. Assume that a=1, then the points on a line are (10,0) and (0,1). This line with a=1 intercepts the circle at 2 points. Since it intercepts the circle at 2 points, there must be other lines with a>1 that still intercept the circle. Howerver, as value of a increases, a line shifts to the right and up...eventually it will be tangent to the circle and then outside the circle...hard to explain without graph... Since we do not know the value of a, three options possible for a>1: 1) the line intercepts the circle at 2 points 2) the line is tangent to the circle 3) the line is outside the circle. Since we do not know the exact value for a, we can't determine if the line intercepts the circle. I would say both statement are not sufficient - answer E

Re: Circle C and line k lie in the xy plane [#permalink]
29 Mar 2011, 06:54

I made a mistake coz I read the x intercept to be 2, don't ask me how -- Anyhow, for those who cannot visualize, here is an excellent free tool http://graph-plotter.cours-de-math.eu/

Once we increase the x intercept, the graph will star moving up, therefore the correct asnwer is E.

Re: Circle C and line k lie in the xy plane [#permalink]
19 May 2011, 14:11

The line x=1 is tangent to the circle at x axis. Any verticale line x>1 would not touch the circle. Any line that is not verticle with x interecept of 1 will intersect the circle at two different places. Since we have a line with -1/10 slope and x interecept that can be very close 1, it might or might not touch based on it's x interecept. Not suff!

Re: Circle C and line k lie in the xy plane. If center of C lie [#permalink]
22 Dec 2011, 10:23

1

This post received KUDOS

If circle C is centered at the origin and has radius 1, does line K intersect circle C?

1. The x-intercept of line k is greater than 1. 2. The slope of line k is -1/10.

Line K will intersect circle C under the following minimum conditions

The x-intercept lies between -1 and 1.

-1 < -b/m < 1

--or--

The y-intercept lies between 1 and -1.

1 > b > -1

Statement 1 allows us to eliminate the first condition. Through the x-intercept formula. Statement 2 does not provide any information about the intercepts.

Taken together, the x-intercept formula allows the deduction

b/.1 > 1

b > .1

that the y-intercept is greater than .1

Is b < 1?

gmatclubot

Re: Circle C and line k lie in the xy plane. If center of C lie
[#permalink]
22 Dec 2011, 10:23

Hello everyone! Researching, networking, and understanding the “feel” for a school are all part of the essential journey to a top MBA. Wouldn’t it be great... ...

Hey Everyone, I am launching a new venture focused on helping others get into the business school of their dreams. If you are planning to or have recently applied...