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Another tricky one

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Another tricky one [#permalink] New post 16 Jun 2008, 20:00
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A
B
C
D
E

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Another tricky one.

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Re: gmatprep 2 Geometry DS [#permalink] New post 16 Jun 2008, 20:12
bsd_lover wrote:
Another tricky one.


I'll go with (B).

To solve it,
BCO = 40
OBC = BCO = 40
BOC = 180 - (BCO + OBC) = 100
ABO = 180 - BCO = 140
BAO = BOA (opposite angles to equal sides) = (180 - 140)/2 = 20

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Re: gmatprep 2 Geometry DS [#permalink] New post 16 Jun 2008, 20:37
bsd_lover wrote:
B is not the OA.


Nice question. Should be (D)
If COD = 60, then OBC = OCB = 30, and the rest follows

+1

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Re: gmatprep 2 Geometry DS [#permalink] New post 16 Jun 2008, 20:49
bsd_lover wrote:
incognito1 wrote:
bsd_lover wrote:
B is not the OA.


Nice question. Should be (D)
If COD = 60, then OBC = OCB = 30, and the rest follows <--- how did you arrive to this ????

+1


COD = OBC + OCB (exterior angle = sum of 2 opposite interior angles)
But since OB = OC (= radius), each equals half of COD = 30

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Re: gmatprep 2 Geometry DS [#permalink] New post 16 Jun 2008, 20:58
COD doesn't look like an exterior angle of triangle COB. COX (as attached ) is the correct exterior angle.

incognito1 wrote:

COD = OBC + OCB (exterior angle = sum of 2 opposite interior angles)
But since OB = OC (= radius), each equals half of COD = 30

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Re: gmatprep 2 Geometry DS [#permalink] New post 16 Jun 2008, 21:14
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bsd_lover wrote:
COD doesn't look like an exterior angle of triangle COB. COX (as attached ) is the correct exterior angle.

incognito1 wrote:

COD = OBC + OCB (exterior angle = sum of 2 opposite interior angles)
But since OB = OC (= radius), each equals half of COD = 30


Nice catch. Try 2 with Answer (D):

BAO = BOA
OBC = BAO + BOA
or, OBC = 2*BOA

OBC = OCB
so, OCB = 2*BOA

COD = BAO + OCB
or, 3*BAO = 60
=> BAO = 20 and OCB = OBC = 40, rest follows...

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Re: gmatprep 2 Geometry DS [#permalink] New post 16 Jun 2008, 23:24
good discussion incognito +1.
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Re: gmatprep 2 Geometry DS [#permalink] New post 17 Jun 2008, 03:11
We can not sure A,B, and C are in line. So C is the best.
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Re: gmatprep 2 Geometry DS [#permalink] New post 17 Jun 2008, 06:33
IMO ans is C.

rephrasing the given info
BAO=x
OCB=a
OBC=b
COD=c
BOA=d

d+b+c=180
d+180-2a+c=180
d=2a-c

In triangle ABO
x+180-a+d=180
x-a+d=0
x=a-d
x=a-(2a-c)
x=c-a

Stmt (1) c=60
we are not sure about a
Stmt (2) a=40
we are not sure about c

Together we have what we are looking for.
This is little time consuming but let me know if this can be done in any faster way.
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Re: gmatprep 2 Geometry DS [#permalink] New post 17 Jun 2008, 12:05
incognito1 wrote:
bsd_lover wrote:
B is not the OA.


Nice question. Should be (D)
If COD = 60, then OBC = OCB = 30, and the rest follows

+1


Can you explain the COD = 60, then OBC = OCB = 30 part

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Re: gmatprep 2 Geometry DS [#permalink] New post 17 Jun 2008, 12:38
brokerbevo wrote:
incognito1 wrote:
bsd_lover wrote:
B is not the OA.


Nice question. Should be (D)
If COD = 60, then OBC = OCB = 30, and the rest follows

+1


Can you explain the COD = 60, then OBC = OCB = 30 part


Actually, that is incorrect (though the answer was inadvertently correct), as bsd_lover pointed out. Refer my next post, I believe that should be correct.

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Re: gmatprep 2 Geometry DS [#permalink] New post 17 Jun 2008, 12:45
beautiful problem! Easy but tricky.
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Re: gmatprep 2 Geometry DS [#permalink] New post 17 Jun 2008, 14:44
me likes triangle..

guys any good source on beefing up my geometery? i struggle with coordinate and advance triangle type of problems..such as the one posted by BSD
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Re: gmatprep 2 Geometry DS [#permalink] New post 17 Jun 2008, 20:46
I cast doubt on the OA. Hypothesis does not tell that A, B, C are in one line.

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Re: gmatprep 2 Geometry DS [#permalink] New post 19 Jun 2008, 09:14
lexis wrote:
I cast doubt on the OA. Hypothesis does not tell that A, B, C are in one line.

Image

Image


Damn good call. Without knowing if AC is a straight line you can't relate BAO to ABO to CBO to BCO... so if the link can't be made and one angle is not enough. But if you bring both pieces of information together you have what you need.
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Re: gmatprep 2 Geometry DS [#permalink] New post 19 Jun 2008, 09:33
To figure out the problem you need Y and X to find Z : Z = 2Y - X. Therefore you need both statements together. Hopefully the picture makes it easier to see.

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Re: gmatprep 2 Geometry DS [#permalink] New post 19 Jun 2008, 14:20
Lexis,
I'd go with what is obvious. Even though the line is not mentioned to be straight, I feel that its clear enough in the diagram.

lexis wrote:
BSD, Do you have any idea?
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Re: gmatprep 2 Geometry DS [#permalink] New post 19 Jun 2008, 23:15
COD=40
COA=140=COB+BOA=COB+BAO
IE: BAO=140-COB
NOW, COB=180-2*(CBO)
OR, COB=180-2*(180-ABO)
OR, COB=180-360+ABO=ABO-180=2*BAO-180
THEREFORE,
BAO=140-2*BAO-180
OR, BAO=40
THEREFORE, (D)
Re: gmatprep 2 Geometry DS   [#permalink] 19 Jun 2008, 23:15
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