Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Oct 27 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. One hour of live, online instruction
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 09 Nov 2012
Posts: 62

A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
15 Oct 2013, 22:17
Question Stats:
26% (02:11) correct 74% (01:58) wrong based on 437 sessions
HideShow timer Statistics
A circle is drawn on a coordinate plane. If a line is drawn through the origin and the center of that circle, is the line’s slope less than 1? (1) No point on the circle has a negative xcoordinate. (2) The circle intersects the xaxis at two different positive coordinates.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58434

A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
16 Oct 2013, 02:02
A circle is drawn on a coordinate plane. If a line is drawn through the origin and the center of that circle, is the line’s slope less than 1? (1) No point on the circle has a negative xcoordinate. This implies that the center of the circle is either in I or IV quadrant AND the x coordinate of the center is greater than the radius of this circle. Still not sufficient. Consider the cases below: Not sufficient. (2) The circle intersects the xaxis at two different positive coordinates. This implies that the distance from the center to the xaxis is less than the radius: Not sufficient. (1)+(2) We know that the center is either in I or IV quadrant. We also know that the x coordinate of the center is greater than the radius of this circle and the distance from the center to the xaxis is less than the radius. This implies that the center is below line y=x, which means that the slope of a line passing origin and the center is less than 1. Sufficient. Answer: C. Attachment:
Untitled2.png [ 13.19 KiB  Viewed 22479 times ]
Attachment:
Untitled.png [ 15.78 KiB  Viewed 22503 times ]
_________________




Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 445
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
Updated on: 16 Oct 2013, 02:41
I believe E should be the answer. Y= mx + c C=0, since line will pass through 0,0 Y = MX M depends upon the sign of Y, From (1) and (2), Y can be negative or positive, Not sure hence E.
Attachments
Y negative.png [ 5.68 KiB  Viewed 19877 times ]
_________________
Like my post Send me a Kudos It is a Good manner.My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html
Originally posted by honchos on 16 Oct 2013, 02:35.
Last edited by honchos on 16 Oct 2013, 02:41, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 58434

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
16 Oct 2013, 02:37
honchos wrote: I believe E should be the answer.
Y= mx + c C=0, since line will pass through 0,0
Y = MX
M depends upon the sign of Y, From (1) and (2), Y can be negative or positive, Not sure hence E. The question asks whether the slope is less than 1. The correct answer is C.
_________________



Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 445
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
Updated on: 16 Oct 2013, 02:42
Bunuel wrote: honchos wrote: I believe E should be the answer.
Y= mx + c C=0, since line will pass through 0,0
Y = MX
M depends upon the sign of Y, From (1) and (2), Y can be negative or positive, Not sure hence E. The question asks whether the slope is less than 1. The correct answer is C. M = Y/X, X is always positive but Y may be Positive or negative, so slope may be +ve or ve... Hence E M: stands for line's slope
_________________
Like my post Send me a Kudos It is a Good manner.My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html
Originally posted by honchos on 16 Oct 2013, 02:40.
Last edited by honchos on 16 Oct 2013, 02:42, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 58434

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
16 Oct 2013, 02:42
honchos wrote: Bunuel wrote: honchos wrote: I believe E should be the answer.
Y= mx + c C=0, since line will pass through 0,0
Y = MX
M depends upon the sign of Y, From (1) and (2), Y can be negative or positive, Not sure hence E. The question asks whether the slope is less than 1. The correct answer is C. M = Y/X, X is always positive but Y may be Positive or negative, so slope may be +ve or ve... Hence E [b]M [/b]: stands for line's slope We are NOT asked whether the slope is negative, we are asked whether the slope is less than 1.
_________________



Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 445
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
16 Oct 2013, 12:16
Got it my bad, misinterpreted the question.
_________________
Like my post Send me a Kudos It is a Good manner.My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Intern
Joined: 07 Apr 2013
Posts: 28
Location: United States
WE: Information Technology (Computer Software)

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
25 Oct 2013, 04:00
Isn't it possible that the circle touches the origin and the radius and the center ( the center lies on the x axis and there is no y coordinate for it) of the circle is same ?



Math Expert
Joined: 02 Sep 2009
Posts: 58434

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
25 Oct 2013, 04:20
pradeepram wrote: Isn't it possible that the circle touches the origin and the radius and the center ( the center lies on the x axis and there is no y coordinate for it) of the circle is same ? If center of the circle is on the xaxis the ycoordinate of the center is 0. In this case the slope of the line will be 0 (since the line would be horizontal), so still less than 1. Also, the circle cannot pass through the origin, because we are told that "the circle intersects the xaxis at two different [u]positive[/u] coordinates".
_________________



Intern
Joined: 07 Apr 2013
Posts: 28
Location: United States
WE: Information Technology (Computer Software)

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
25 Oct 2013, 04:36
Thanks Bunuel.
I considered this option for statement 1 alone. Since this is one of the possibilities, we could also take this into consideration for statement 1 right ?



Manager
Joined: 04 Sep 2012
Posts: 120

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
26 Oct 2013, 04:46
Bunuel wrote: A circle is drawn on a coordinate plane. If a line is drawn through the origin and the center of that circle, is the line’s slope less than 1? (1) No point on the circle has a negative xcoordinate. This implies that the center of the circle is either in I or IV quadrant AND the x coordinate of the center is greater than the radius of this circle. Still not sufficient. Consider the cases below: Attachment: Untitled.png Not sufficient. (2) The circle intersects the xaxis at two different positive coordinates. This implies that the distance from the center to the xaxis is less than the radius: Attachment: Untitled2.png Not sufficient. (1)+(2) We know that the center is either in I or IV quadrant. We also know that the x coordinate of the center is greater than the radius of this circle and the distance from the center to the xaxis is less than the radius. This implies that the center is below line y=x, which means that the slope of a line passing origin and the center is less than 1. Sufficient. Answer: C. Hi Bunuel, As always great explanation, Just one question you said as the center is below line y=x , means that slope of a line is less than 1 how do you come to that conclusion?? I am sorry I am weak in Coordinate geometry so pardon me if I am missing any basic Formulae for Slope .. Regards, Abhinav
_________________
Regards, Abhinav
GMAT 1  580 (Q47 V23) http://gmatclub.com/forum/atightslaponface149457.html
GMAT 2  670 (Q48 V34) http://gmatclub.com/forum/670onemonthofffromofficeand2monthshardwork163761.html#p1297561
“If you don't change your life; your life will change you.”



Intern
Status: Joining Cranfield Sep 2014
Joined: 01 Sep 2012
Posts: 49
Concentration: Technology, General Management
GMAT 1: 530 Q50 V14 GMAT 2: 630 Q48 V29
WE: Engineering (Energy and Utilities)

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
27 Oct 2013, 05:56
abhinav11 wrote: Bunuel wrote: A circle is drawn on a coordinate plane. If a line is drawn through the origin and the center of that circle, is the line’s slope less than 1? (1) No point on the circle has a negative xcoordinate. This implies that the center of the circle is either in I or IV quadrant AND the x coordinate of the center is greater than the radius of this circle. Still not sufficient. Consider the cases below: Attachment: Untitled.png Not sufficient. (2) The circle intersects the xaxis at two different positive coordinates. This implies that the distance from the center to the xaxis is less than the radius: Attachment: Untitled2.png Not sufficient. (1)+(2) We know that the center is either in I or IV quadrant. We also know that the x coordinate of the center is greater than the radius of this circle and the distance from the center to the xaxis is less than the radius. This implies that the center is below line y=x, which means that the slope of a line passing origin and the center is less than 1. Sufficient. Answer: C. Hi Bunuel, As always great explanation, Just one question you said as the center is below line y=x , means that slope of a line is less than 1 how do you come to that conclusion?? I am sorry I am weak in Coordinate geometry so pardon me if I am missing any basic Formulae for Slope .. Regards, Abhinav Dear Abhinav; The standard equation of the line is y= mx + c, It is given that the line passes through origin, so coordinate will be (0, 0). To satisfy the condition given i.e. (0,0), you will find the modified equation as y= mx now the question is asking whether m < 1. if you assume m=1, you will find a straight line y = x, you will find this line bisects (45 deg) the first quadrant, try to solve the question by drawing, you will understand it much better. in equation y = x, each value of y is equal to x Now coming to question, for m to be less than 1, if you shift the center of circle below the line y= x, then in new equation of line y=mx, for every value of y, you will have greater corresponding value of x, which indeed is the condition we are looking for y / x < 1. Similarly, if you shift the center of circle above the line y=x, then in new equation of line y=mx, for every value of y, you will lower corresponding value of x. If you did not get what I am trying to explain, try to draw this and you will understand.



Intern
Status: Waiting for Decisions
Joined: 23 Dec 2012
Posts: 39
Location: India
Sahil: Bansal
GMAT 1: 570 Q49 V20 GMAT 2: 690 Q49 V34
GPA: 3
WE: Information Technology (Computer Software)

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
27 Oct 2013, 06:47
Bunuel wrote: A circle is drawn on a coordinate plane. If a line is drawn through the origin and the center of that circle, is the line’s slope less than 1? (1) No point on the circle has a negative xcoordinate. This implies that the center of the circle is either in I or IV quadrant AND the x coordinate of the center is greater than the radius of this circle. Still not sufficient. Consider the cases below: Attachment: Untitled.png Not sufficient. (2) The circle intersects the xaxis at two different positive coordinates. This implies that the distance from the center to the xaxis is less than the radius: Attachment: Untitled2.png Not sufficient. (1)+(2) We know that the center is either in I or IV quadrant. We also know that the x coordinate of the center is greater than the radius of this circle and the distance from the center to the xaxis is less than the radius. This implies that the center is below line y=x, which means that the slope of a line passing origin and the center is less than 1. Sufficient. Answer: C. Hi Bunuel, Please explain the point " the x coordinate of the center is greater than the radius of this circle", which you have derived from statement 1 Thanks, Sahil



Intern
Joined: 15 Jul 2012
Posts: 35

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
27 Oct 2013, 10:42
Bunuel wrote: A circle is drawn on a coordinate plane. If a line is drawn through the origin and the center of that circle, is the line’s slope less than 1? (1) No point on the circle has a negative xcoordinate. This implies that the center of the circle is either in I or IV quadrant AND the x coordinate of the center is greater than the radius of this circle. Still not sufficient. Consider the cases below: Attachment: Untitled.png Not sufficient. (2) The circle intersects the xaxis at two different positive coordinates. This implies that the distance from the center to the xaxis is less than the radius: Attachment: Untitled2.png Not sufficient. (1)+(2) We know that the center is either in I or IV quadrant. We also know that the x coordinate of the center is greater than the radius of this circle and the distance from the center to the xaxis is less than the radius. This implies that the center is below line y=x, which means that the slope of a line passing origin and the center is less than 1. Sufficient. Answer: C. Can this be proven algebracilly, Second I have not understood your statement "AND the x coordinate of the center is greater than the radius of this circle". and also this statement " . This implies that the distance from the center to the xaxis is less than the radius"Please help and tell how to approach the problem as there will be no graphs available in the test...



Intern
Joined: 15 Jul 2012
Posts: 35

A circle is drawn on a coordinate plane. If a line is drawn.
[#permalink]
Show Tags
28 Oct 2013, 07:34
A circle is drawn on a coordinate plane. If a line is drawn through the origin and the center of that circle, is the line’s slope less than 1?
(1) No point on the circle has a negative xcoordinate.
(2) The circle intersects the xaxis at two different positive coordinates.
Can this be proven algebraically, Second I have not understood your statement "AND the x coordinate of the center is greater than the radius of this circle". and also this statement ". This implies that the distance from the center to the xaxis is less than the radius" Please help and tell how to approach the problem….



Intern
Joined: 10 Aug 2013
Posts: 13
Location: United States

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
09 Apr 2015, 00:21
Bunuel wrote: A circle is drawn on a coordinate plane. If a line is drawn through the origin and the center of that circle, is the line’s slope less than 1? (1) No point on the circle has a negative xcoordinate. This implies that the center of the circle is either in I or IV quadrant AND the x coordinate of the center is greater than the radius of this circle. Still not sufficient. Consider the cases below: Attachment: Untitled.png Not sufficient. (2) The circle intersects the xaxis at two different positive coordinates. This implies that the distance from the center to the xaxis is less than the radius: Attachment: Untitled2.png Not sufficient. (1)+(2) We know that the center is either in I or IV quadrant. We also know that the x coordinate of the center is greater than the radius of this circle and the distance from the center to the xaxis is less than the radius. This implies that the center is below line y=x, which means that the slope of a line passing origin and the center is less than 1. Sufficient. Answer: C. Is there any other way of doing this question.When I'm considering both together.I am not able to confidently visualize it.



NonHuman User
Joined: 09 Sep 2013
Posts: 13316

Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
Show Tags
08 Jul 2019, 03:58
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: A circle is drawn on a coordinate plane. If a line is drawn
[#permalink]
08 Jul 2019, 03:58






