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A circle is drawn on a coordinate plane. If a line is drawn
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15 Oct 2013, 21:17
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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.
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A circle is drawn on a coordinate plane. If a line is drawn
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16 Oct 2013, 01:02
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:
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Re: A circle is drawn on a coordinate plane. If a line is drawn
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Updated on: 16 Oct 2013, 01:41
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.
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Originally posted by honchos on 16 Oct 2013, 01:35.
Last edited by honchos on 16 Oct 2013, 01:41, edited 1 time in total.



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Re: A circle is drawn on a coordinate plane. If a line is drawn
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16 Oct 2013, 01:37



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Re: A circle is drawn on a coordinate plane. If a line is drawn
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Updated on: 16 Oct 2013, 01:42
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
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Originally posted by honchos on 16 Oct 2013, 01:40.
Last edited by honchos on 16 Oct 2013, 01:42, edited 1 time in total.



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Re: A circle is drawn on a coordinate plane. If a line is drawn
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16 Oct 2013, 01:42
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.
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Re: A circle is drawn on a coordinate plane. If a line is drawn
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16 Oct 2013, 11:16
Got it my bad, misinterpreted the question.
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Re: A circle is drawn on a coordinate plane. If a line is drawn
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25 Oct 2013, 03:00
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 ?



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Re: A circle is drawn on a coordinate plane. If a line is drawn
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25 Oct 2013, 03:20



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Re: A circle is drawn on a coordinate plane. If a line is drawn
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25 Oct 2013, 03:36
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 ?



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Re: A circle is drawn on a coordinate plane. If a line is drawn
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26 Oct 2013, 03:46
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
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Re: A circle is drawn on a coordinate plane. If a line is drawn
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27 Oct 2013, 04:56
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.



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Re: A circle is drawn on a coordinate plane. If a line is drawn
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27 Oct 2013, 05:47
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



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Re: A circle is drawn on a coordinate plane. If a line is drawn
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27 Oct 2013, 09:42
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...



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A circle is drawn on a coordinate plane. If a line is drawn.
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28 Oct 2013, 06:34
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….



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Re: A circle is drawn on a coordinate plane. If a line is drawn
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08 Apr 2015, 23:21
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.



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