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GEOMETRY-gmatprep

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Senior Manager
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GEOMETRY-gmatprep [#permalink] New post 29 Dec 2008, 08:25
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

71% (01:56) correct 29% (01:23) wrong based on 13 sessions
Attachment:
qs.jpg
qs.jpg [ 29.05 KiB | Viewed 2471 times ]


Can someone pls help with this question?
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Re: GEOMETRY-gmatprep [#permalink] New post 31 Dec 2008, 01:03
D

from the question we can know,

AB = OC ---1)
BO = OC ---2) since both are radius.
it makes triangle BOC and triangle BAO isoseles.

lets take BAO = BOA = x ----- 3)
CBO = BCO = a ------ 4)
BOC = y
ABO = z

Stmt1:
COD is 60

so we can say x+y = 120 -------(5) (from the line AD)
also, z+a = 180 --------------(6)
from triangle BAO,
2x+z = 180 --------------(7)
from triangle BOC,
2a +y = 180 ---------------(8)

solving (6), (7), and (8) we get,
4x+y = 180 ---- (9)

from (5) and (9) we get
x = 20 which is BAO --- SO SUFF.

stmt 2:
this gives more close clue that a= 40 by using isoles triangle propety we get x = 20.
SUFF

so D
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Re: GEOMETRY-gmatprep [#permalink] New post 31 Dec 2008, 02:24
D .

(1) 60=BCO+A
=CBO+A
=(A+BOA)+A (A=BOA)
=2A+A=3A
A=20

(2) BCO=40
CBO=40
A+BOA=40
2A=40 (A=BAO)
A=20.
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Re: GEOMETRY-gmatprep [#permalink] New post 26 May 2009, 22:30
I have a question: How can you assume ABC is a straight line?

That's breaking the most fundamental GMAT rule-- assuming a shape is drawn properly!

I did this question and came to C, I know the answer is D, but how can you just assume that ABC is straight and hence we can sum up the angles to 180 on it?

See my attached schematic... if we don't assume ABC is straight, then the answer is C as my diagram shows that the shapes change.
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Re: GEOMETRY-gmatprep [#permalink] New post 22 Oct 2009, 06:52
2
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1st step: Write down data and assign variables:
BAO = BOA = x
CBO = BCO = a
BOC = y
ABO = z
COD = b

2nd step: Write down the possible equations:
1) Triangle BAO: 180=z+2x
2) Triangle BOC: 180=y+2a
3) Line AOD: 180=x+y+b
4) Line ABC: 180=z+a
-> 4 equations & 5 variables.

Stat1: gives the value of b -> 4 equations & 4 variables -> we can solve for x: sufficient

Stat2: gives the value of a -> 4 equations & 4 variables (or 3 & 3, as equation 3 becomes unnecesary) -> we can solve for x: sufficient

Now, if as Hades said, ABC is not a line, then equation 4 dissapears, and we need both a and b to solve for x -> answer would be C. But this is an official gmat prep problem, so I guess the OA must be right, and OA is D.

Could somebody help determine how could the answer be D without the assumption that ABC is a line?
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Re: GEOMETRY-gmatprep   [#permalink] 22 Oct 2009, 06:52
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