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Updated on: 02 Apr 2019, 03:36
Originally posted by vigneshpandi on 21 Sep 2010, 21:28.
Last edited by Bunuel on 02 Apr 2019, 03:36, edited 2 times in total.
Last edited by Bunuel on 02 Apr 2019, 03:36, edited 2 times in total.
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E
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Circle C and line K lie in the XY plane. If circle C is centered at the orgin and has a 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
(1) The X-Intercept of line k is greater than 1
(2) The slope of line k is -1/10
21 Sep 2010, 21:56
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Circle C and line K lie in the XY plane. If circle C is centered at the origin and has a radius 1, does line K intersect circle C?
The best way to solve this question would be to visualize/draw it.
No matter what the slope is, it’s possible for line not to cross the circle as the x intercept can be + infinite.
(1) The X-Intercept of line k is greater than 1 --> Just says that X-intercept is to the right of the circle. Not sufficient
(2) The slope of line k is -1/10 --> Just says that slope is negative -1/10 --> line is just going down. Not sufficient.
(1)+(2) As we don't know exact intercept of line and X-axis we can not determine whether line intersects the circle or not. Not sufficient.
To elaborate more: we can draw infinitely many parallel lines with X-intercept more than 1 and slope -1/10, some will intersect the circle (for example line with X-intercept 1.1) and some not (for example line with X-intercept 1,000,000). Check the image below for two possible scenarios: blue line (with the slope of -1/10 and the x-Intercept greater than 1) intersects the circle while the red line (also with the slope of -1/10 and the x-Intercept greater than 1) does not.
Answer: E.
For more on this issue check Coordinate Geometry Chapter of Math Book: https://gmatclub.com/forum/math-coordina ... 87652.html
Hope it helps.
graph.png [ 15.11 KiB | Viewed 51817 times ]
The best way to solve this question would be to visualize/draw it.
No matter what the slope is, it’s possible for line not to cross the circle as the x intercept can be + infinite.
(1) The X-Intercept of line k is greater than 1 --> Just says that X-intercept is to the right of the circle. Not sufficient
(2) The slope of line k is -1/10 --> Just says that slope is negative -1/10 --> line is just going down. Not sufficient.
(1)+(2) As we don't know exact intercept of line and X-axis we can not determine whether line intersects the circle or not. Not sufficient.
To elaborate more: we can draw infinitely many parallel lines with X-intercept more than 1 and slope -1/10, some will intersect the circle (for example line with X-intercept 1.1) and some not (for example line with X-intercept 1,000,000). Check the image below for two possible scenarios: blue line (with the slope of -1/10 and the x-Intercept greater than 1) intersects the circle while the red line (also with the slope of -1/10 and the x-Intercept greater than 1) does not.
Answer: E.
For more on this issue check Coordinate Geometry Chapter of Math Book: https://gmatclub.com/forum/math-coordina ... 87652.html
Hope it helps.
Attachment:
graph.png [ 15.11 KiB | Viewed 51817 times ]
09 Nov 2010, 05:56
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anilnandyala
circle c & line k lie in xy-plane. if circle c is centered at the origin & has a radius 1 . does line k intersect circle c?
1 the x intercept of line k>1
2 the slope of line k= -(1/10)
1 the x intercept of line k>1
2 the slope of line k= -(1/10)
Look at the diagrams.
Statement 1: If x intercept > 1, the line can be any of the following (and can be drawn in many more ways)
Attachment:
Ques.jpg [ 16.54 KiB | Viewed 48649 times ]
Statement 2: If slope = -1/10, the line can be drawn in any of the following ways. (and many more)
Attachment:
Ques1.jpg [ 14.73 KiB | Viewed 48322 times ]
Using both together: Look at the diagrams above. Both have x intercepts greater than 1 and slope = -1/10. In one case, it will intersect the circle, in the other case, it will not. SO both statements together are not sufficient. Answer (E).
