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by dumb.doofus » Mon May 25, 2009 8:32 pm
I think it should be 1. i.e. s = 1

Might be there is a quicker solution..

anyways,

PO = 2

=> s^2 + t^2 = 4 --------- (1)

also PQ = (s+root(3))^2 + (t-1)^2 = 8 ---------- (2)

substitute (1) in (2) we get

root(3)s = t ---------- (3)

substitute (3) in (1)

we get s = 1
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by Brent@GMATPrepNow » Mon May 25, 2009 8:45 pm
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by vittalgmat » Mon May 25, 2009 11:13 pm
Brent Hanneson wrote:Image
Hi Brent,
I am trying to understand how your solution can answer the question..
I guess there might have been a mistake !! ;-)

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by Svedankae » Tue May 26, 2009 6:30 am
anyone attack this problem by seeing the two 30,60,90 triangles? or did u all do it dumbdoofus' way?
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by ssmiles08 » Tue May 26, 2009 7:08 am
Yes there are 2 30-60-90 triangles.

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by Brent@GMATPrepNow » Tue May 26, 2009 9:05 am
vittalgmat wrote:
Brent Hanneson wrote:Image
Hi Brent,
I am trying to understand how your solution can answer the question..
I guess there might have been a mistake !! ;-)

rgds
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Oops, I uploaded the wrong image :D
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by Brent@GMATPrepNow » Tue May 26, 2009 9:07 am
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by dtweah » Tue May 26, 2009 9:23 am
Svedankae wrote:anyone attack this problem by seeing the two 30,60,90 triangles? or did u all do it dumbdoofus' way?
No. It is invalid to use 30 60 90 or 45 45 90. Since angle QOB= angle OPA ( see diagram for proof) you cannot such a logic. If Angle QOB= 30, you have a 30 60 90. If QOB =45, you have a 45 45 90 scenario. Since there is no way of knowing what angle QOB is, you can't use the 30 60 90 argument. This argument can only be used if you can show that the angle QOB =30. In geometry, we cannot assume an angle has x or y degree. We have to prove it.
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by dumb.doofus » Tue May 26, 2009 10:56 am
dtweah wrote:
Svedankae wrote:anyone attack this problem by seeing the two 30,60,90 triangles? or did u all do it dumbdoofus' way?
No. It is invalid to use 30 60 90 or 45 45 90. Since angle QOB= angle OPA ( see diagram for proof) you cannot such a logic. If Angle QOB= 30, you have a 30 60 90. If QOB =45, you have a 45 45 90 scenario. Since there is no way of knowing what angle QOB is, you can't use the 30 60 90 argument. This argument can only be used if you can show that the angle QOB =30. In geometry, we cannot assume an angle has x or y degree. We have to prove it.
Hi dtweah,

I really dont think that what you mentioned is correct. I think we can prove that angle POA is 30 degrees and angle QOB is 60.. please check the picture.


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by Brent@GMATPrepNow » Tue May 26, 2009 11:05 am
Nice graphic, DD. I love the drop shadows!!
You're certainly taking it up a notch :D
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by dumb.doofus » Tue May 26, 2009 11:19 am
Brent Hanneson wrote:Nice graphic, DD. I love the drop shadows!!
You're certainly taking it up a notch :D
LOL.. :-) thanks Brent.. it's just the software application. I have not spent more time on creating the shadows :-)
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by Svedankae » Tue May 26, 2009 11:40 am
thanks everybody! :)
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by dtweah » Tue May 26, 2009 12:44 pm
dumb.doofus wrote:
dtweah wrote:
Svedankae wrote:anyone attack this problem by seeing the two 30,60,90 triangles? or did u all do it dumbdoofus' way?
No. It is invalid to use 30 60 90 or 45 45 90. Since angle QOB= angle OPA ( see diagram for proof) you cannot such a logic. If Angle QOB= 30, you have a 30 60 90. If QOB =45, you have a 45 45 90 scenario. Since there is no way of knowing what angle QOB is, you can't use the 30 60 90 argument. This argument can only be used if you can show that the angle QOB =30. In geometry, we cannot assume an angle has x or y degree. We have to prove it.
Hi dtweah,

I really dont think that what you mentioned is correct. I think we can prove that angle POA is 30 degrees and angle QOB is 60.. please check the picture.


Image
Yes it can be proven Brent. you showed it in your earlier post. I withdraw my previoius comment. I have fallen into the habit of avoiding giving angles values until I am doubly sure. I have identified that as a GMAT TRAP but fell victim to my own fears. You really draw nice diagrams!!
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