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bacali: Master | Next Rank: 500 Posts; Posts: 245; Joined: Thu Aug 16, 2007 12:41 pm

by bacali » Sat Dec 06, 2008 12:57 pm

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Source: Beat The GMAT — Data Sufficiency | Sat Dec 06, 2008 12:57 pm

bacali: Master | Next Rank: 500 Posts; Posts: 245; Joined: Thu Aug 16, 2007 12:41 pm

by bacali » Mon Dec 08, 2008 8:48 am

anyone willing to give it a shot?

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muzali: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Fri Sep 28, 2007 10:16 am; Thanked: 6 times; GMAT Score:710

by muzali » Mon Dec 08, 2008 10:27 am

AB=OC (given) and OC=OB (since both are radii of the semicircle)
=> AB=OC=OB
=>angles BAO=BOA=OBC=OCB=x (angles opposite equal sides)
We need to find x.

1. COD is 60
BOA+BOC+COD=180 (supplementary angles)
x+(180-2x)+60=180
We can find x, so STM 1 is suff.

2.BCO=40
i.e. x =40
STM 2 is suff.

So answer is D

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earth@work: Master | Next Rank: 500 Posts; Posts: 248; Joined: Mon Aug 11, 2008 9:51 am; Thanked: 13 times

by earth@work » Mon Dec 08, 2008 2:16 pm

muzali wrote:AB=OC (given) and OC=OB (since both are radii of the semicircle)
=> AB=OC=OB
=>angles BAO=BOA=OBC=OCB=x (angles opposite equal sides)
We need to find x.

i guess angles BAO=BOA=x & OBC=OCB=y; and x might not be equal to y (do correct me if m wrong here)
1. COD is 60 degrees, we get angle AOC=120, x+y+120=180.......(1)
in triangle ABO, angle ABO=180-y, therefore 2x+(180-y)=180 i.e 2x=y.......(2) we have two variables and two equations- sufficient
2.BCO=40
angle AOC=x+(180-2y)=x+100, now in triangle AOC: x+40+(x+100)=180, so we get val of x---sufficient
answer D

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ch0719: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Mon May 26, 2008 4:12 pm

by ch0719 » Mon Dec 08, 2008 2:22 pm

muzali wrote:AB=OC (given) and OC=OB (since both are radii of the semicircle)
=> AB=OC=OB
=>angles BAO=BOA=OBC=OCB=x (angles opposite equal sides)
We need to find x.

1. COD is 60
BOA+BOC+COD=180 (supplementary angles)
x+(180-2x)+60=180
We can find x, so STM 1 is suff.

2.BCO=40
i.e. x =40
STM 2 is suff.

So answer is D

the answer is D, however OBC=OCB= 2x ... instead of =x

so STM1 should be:
x+(180-4x)+60=180x
and x=20 imo

STM2 is correct

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pbanavara: Master | Next Rank: 500 Posts; Posts: 279; Joined: Wed Sep 24, 2008 8:26 am; Location: Portland, OR; Thanked: 6 times

by pbanavara » Mon Dec 08, 2008 6:25 pm

ch0719 wrote:
muzali wrote:AB=OC (given) and OC=OB (since both are radii of the semicircle)
=> AB=OC=OB
=>angles BAO=BOA=OBC=OCB=x (angles opposite equal sides)
We need to find x.

1. COD is 60
BOA+BOC+COD=180 (supplementary angles)
x+(180-2x)+60=180
We can find x, so STM 1 is suff.

2.BCO=40
i.e. x =40
STM 2 is suff.

So answer is D
the answer is D, however OBC=OCB= 2x ... instead of =x

so STM1 should be:
x+(180-4x)+60=180x
and x=20 imo

STM2 is correct

yep x=20

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