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Source: Beat The GMAT — Data Sufficiency |
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muzali
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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
=> 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
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i guess angles BAO=BOA=x & OBC=OCB=y; and x might not be equal to y (do correct me if m wrong here)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 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
the answer is D, however OBC=OCB= 2x ... instead of =xmuzali 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
so STM1 should be:
x+(180-4x)+60=180x
and x=20 imo
STM2 is correct
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pbanavara
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yep x=20ch0719 wrote:the answer is D, however OBC=OCB= 2x ... instead of =xmuzali 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
so STM1 should be:
x+(180-4x)+60=180x
and x=20 imo
STM2 is correct
