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Geometry -Interesting Q

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by baladon99 » Thu May 05, 2011 12:24 pm
Circle C and line K lie in the xy plane. 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
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu May 05, 2011 2:29 pm
baladon99 wrote:Circle C and line K lie in the xy plane. 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
X-intercept is greater than 1, slope = -1/10, line k intersects circle C:

Image

X-intercept is greater than 1, slope = -1/10, line k does not intersect circle C:

Image

Thus, the 2 statements combined are insufficient to determine whether line k intersects circle C.

The correct answer is E.
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by MAAJ » Thu May 05, 2011 2:48 pm
Lemme give it a try...

Circle: x² + y² = 1

(1) The x intercept of line k is greater than 1
y = mx + b
0 = m * GT(1) + b
When y is 0, x is greater than 1. But we can't determine if line K intersect circle C.

(2) The slope of line K is -1/10
y = -1/10x + b, we know that the line is a diagonal descending from left to right. But we still can't determine if line K intersect circle C

(3) Combined:
0 = -1/10x + b
0 = -x + 10b
-10b = -x
10b = x but we know that when y = 0 then x > 1 so:
10b = x > 1
10b > 1
b > 1/10
With this we know that the y intercept is greater than 1/10
If we draw a line from x-intercept to y-intercept we still can't be sure if line K intercepts circle C

IMO [spoiler](E)[/spoiler]
baladon99 wrote:Circle C and line K lie in the xy plane. 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
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by baladon99 » Sat May 07, 2011 4:40 am
Thanks Guys . In particular GnatGuruNY 's solution is easy to understand for me :)
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