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three space question? OG (11ed) question incorrect.

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Source: OG (11ed) p25 #36 (Diagnostic)

If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?
1) The length of the line segment XY is 3
2) The length of the line segment OY is 1.5

Answer: B (#2 is sufficient)

My Answer: E - while X and Y are on the same plane, you are not told if circle C exists on that same plane. You can easily imagine two planes intersecting where the point X on plane 1 is contained in the circle on plane 2 while point Y is not. The key here is that they introduced the idea of three dimensional plotting with the use of 'planes'. For the answer they propose you must assume that the circle and the points are on the same plane - which is not clear in the question. (If you are having a hard time visualizing this, see https://en.wikipedia.org/wiki/Image:Plan ... ection.png)

I suspect that I am simply over thinking the problem as I have a background in mathematics and have to work in three space from time to time. Is it a safe assumption that 3 space cartesian questions won't be found on the test and this question is just poorly written?

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by Vasudha » Sun Mar 11, 2007 7:25 pm

Although the question does not explicitly state that the circle is in the same plane as points X and Y, it can be inferred that the circle is in the same plane because the question clearly states that point X lies inside the circle. Therefore the circle, point x, and point y are in the same plane and B is correct.

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by colinbendell » Sun Mar 11, 2007 8:00 pm
That's not true. Point X can be at the point of intersection and therefore be present in two planes. This has no bearing on the location of point Y.

Try this experiment to demonstrate the problem at hand. Take two hair combs (the simple black kind) and on the first draw a circle. On the second pick two points X and Y. Now make the two combs intersect so that point X is somewhere in the circle on the first comb. The problem should be quite evident - in three space this problem is not solvable with the data at hand.


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by Stacey Koprince » Sun Mar 11, 2007 10:59 pm
This is really a case of you know too much and it hurt you. :) This test really does just go up to high-school level Algebra 2. Seriously advanced math that might address various things differently just doesn't get tested here. So, yes, don't worry about it!
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it 'should' be E

by benjaminvw » Wed Feb 11, 2009 12:34 pm
My answer was E as well, it does not state that the circle is in the same plane, it could just as easily cut through the plane of X and Y right at point X. I should say that unlike the first poster I don't know very advanced math and haven't done geometry since high school.

Not a good question and it leaves me not knowing how to handle such an issue on test day.

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Re: it 'should' be E

by x2suresh » Wed Feb 11, 2009 12:54 pm
agree with B.

OY =1.5 <2.. definitely it is inside the circle.


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by Ian Stewart » Wed Feb 11, 2009 4:53 pm
If the GMAT is testing 3-dimensional geometry, this will be made very clear in the question. Otherwise, you should assume you're working in plane (2-d) geometry. Good point about the question above, though - the wording really should be more clear here. The test should not be punishing those who know too much!
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