Problem Solving

Hi Attached, can someone please provide a solution to the problem.

Thanks.

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

Brent Hanneson wrote:

Hi Brent,
I am trying to understand how your solution can answer the question..
I guess there might have been a mistake !!

rgds
-V

anyone attack this problem by seeing the two 30,60,90 triangles? or did u all do it dumbdoofus' way?

Yes there are 2 30-60-90 triangles.

https://www.beatthegmat.com/what-is-the- ... 27181.html

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.

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.

Brent Hanneson wrote:Nice graphic, DD. I love the drop shadows!!
You're certainly taking it up a notch

LOL.. thanks Brent.. it's just the software application. I have not spent more time on creating the shadows

thanks everybody!

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.

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!!