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RonPurewal
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Post subject:  Posted: Tue Jul 29, 2008 4:54 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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Guest660 wrote: Confusion regarding this problem...
we know that each triangle is 30 60 90 ....
also that radius is 2... so if we draw a line joining both the points...we form a triangle... with sides equal(radius)...
each angle is 45 ..
now - is this correct.... that means my total sum of angels is not 90 for the angel p.. between a line joining pint p to q and a perpendicular to x axis...
am i missing something ??
no, you're not missing anything.
the problem is that the diagram is not drawn to scale. (if it were, it would be easy to infer the coordinates, because you could just equate the known distances with any unknown distances: i.e., because of the symmetry of the problem, anything looking like the known "1" could be assumed to be 1, and anything looking like the known "√3" could be assumed to be √3.
in reality, the diagram is nowhere near being symmetrical with respect to the y-axis. therefore, the segment connecting p and q is not parallel to the x-axis, and so you are correct that the designated angle would NOT be 90 degrees.
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guy.b
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Post subject: Re: GMAT Prep - Geometry (2) Posted: Sat Jul 31, 2010 7:37 am |
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Posts: 6
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Hi,
I understand the solution BUT the figure (posted in the beginning of this thread) is confusing. When I read the question and saw the image I immediately answered S=sqrt(3).
Why the authors of the question didn't add the comment "figure not drawn to scale"? How should I use the figures in Geometry problems in the GMAT? Can I make assumption based on figures?
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RonPurewal
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Post subject: Re: GMAT Prep - Geometry (2) Posted: Thu Aug 05, 2010 9:23 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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guy.b wrote: Hi,
I understand the solution BUT the figure (posted in the beginning of this thread) is confusing. When I read the question and saw the image I immediately answered S=sqrt(3).
Why the authors of the question didn't add the comment "figure not drawn to scale"? How should I use the figures in Geometry problems in the GMAT? Can I make assumption based on figures? yeah -- they should have included that warning. i'm not sure why they didn't. however, if there's one thing i could tell you about guessing answers on this test, it would be this: if you think that you can solve a gmat problem in less than ten seconds, your solution is probably wrong.there are exceptions to this rule -- for instance, if you know some really obscure fact or shortcut -- but, if you just think "hey, symmetry, i'm done!", then it's a pretty safe bet that you're picking a "sucker answer".
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chaouky
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Post subject: Re: GMAT Prep - Geometry (2) Posted: Tue Apr 05, 2011 10:21 am |
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hi,
there is something I don't get here :
we have OPQ a rectangle triangle isocele with OP=OQ=2
and PQ = sqrt(8) = 2*sqrt2)
Why don't we have s = sqrt(8) - sqrt (3) ??
Thanks !!
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tim
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Post subject: Re: GMAT Prep - Geometry (2) Posted: Tue Apr 05, 2011 6:39 pm |
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| ManhattanGMAT Staff |
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Posts: 2242
Location: Southwest Airlines, seat 21C
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PQ is not a horizontal line..
_________________
Tim Sanders
Manhattan GMAT Instructor
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Buix0065
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Post subject: Re: GMAT Prep - Geometry (2) Posted: Sun Sep 25, 2011 1:01 pm |
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Hello, What got me on this problem--and I think will get me on any similar problem is that both lines start from (0,0) which is the center point of the circle. If this is the case, from center point to the edge is the radius right? So I would assume OP = OQ Then, since <POQ is a 90 degree angle, OP and OQ are same length and same angle, so P and Q must be same distance from 0. Please let me know what I'm missing so I don't make this mistake again!
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RonPurewal
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Post subject: Re: GMAT Prep - Geometry (2) Posted: Thu Oct 06, 2011 5:50 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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Buix0065 wrote: Hello, What got me on this problem--and I think will get me on any similar problem is that both lines start from (0,0) which is the center point of the circle. If this is the case, from center point to the edge is the radius right? So I would assume OP = OQ Then, since <POQ is a 90 degree angle, OP and OQ are same length and same angle, so P and Q must be same distance from 0. Please let me know what I'm missing so I don't make this mistake again! actually, nothing that you wrote there is wrong -- the two points really are the same distance away from the origin. the problem, though, is that the problem isn't asking for a distance from the origin; the problem is only asking for one coordinate (namely, the x-coordinate). therefore, the problem has little to do with distance from the origin. for instance, (5, 0) and (4, 3) are both 5 units away from the origin, but none of their coordinates are the same.
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hsgross
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Post subject: Re: GMAT Prep - Geometry (2) Posted: Tue Feb 07, 2012 5:55 am |
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| Course Students |
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Posts: 1
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Isn't the easiest way to complete this problem simply by recognizing that there are two perpendicular lines (angle =90) so then to find point (s,t) we can just use the reciprocal slope, which would leave us with 1 for s?
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RonPurewal
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Post subject: Re: GMAT Prep - Geometry (2) Posted: Thu Feb 09, 2012 8:09 pm |
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| ManhattanGMAT Staff |
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Posts: 7146
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hsgross wrote: Isn't the easiest way to complete this problem simply by recognizing that there are two perpendicular lines (angle =90) so then to find point (s,t) we can just use the reciprocal slope, which would leave us with 1 for s? it makes no difference what is the “easiest” way to solve the problem; your only goal should be to learn as many ways as possible to solve it. (“easiest” is a meaningless judgment on a forum like this one anyway, because judgments of what is easy and what is hard will vary considerably from individual to individual.)
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