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# GMATPrep geometry In the figure shown, point O is the center

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GMATPrep geometry In the figure shown, point O is the center [#permalink]  05 Nov 2006, 19:57
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GMATPrep geometry

In the figure shown, point O is the center of the semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?

(1) The degree measure of angle COD is 60

(2) The degree measure of angle BCO is 40
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Last edited by kidderek on 05 Nov 2006, 20:35, edited 1 time in total.
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Since AB = OC (radius) it also = OB(this is also the radius)

So ABO is a isoceles triangle

Nthe angle opp to these 2 sides OA and AB are equal since their sides are equal

So Angle O = Angle A

Now coming to 1) COD =60 INSUFF

2) BCO = 40 this is INSUFF too

But if you combine 'em

Angle B +Angle C =Angle COD =60

Since C=40 from(2) angle CBO=20 in triangle CBO

So angle ABO = 160

The other sides neing equal they are 10 apiece

So C
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Re: GMATPrep geometry [#permalink]  05 Nov 2006, 20:44
Why is B insuff?

If angle BCO=40, angle CBO=40 b/c triangle BCO is isosceles, with legs BO=CO (each is a radius of the semicircle)

If angle CBO=40, then angle ABO=140

triangle ABO=isosceles with AB=BO

therefore, angle BAO=BOA=20
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Re: GMATPrep geometry [#permalink]  05 Nov 2006, 21:01
kidderek wrote:
Why is B insuff?

If angle BCO=40, angle CBO=40 b/c triangle BCO is isosceles, with legs BO=CO (each is a radius of the semicircle)

If angle CBO=40, then angle ABO=140

triangle ABO=isosceles with AB=BO

therefore, angle BAO=BOA=20

Yep...B should be enough...
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Re: GMATPrep geometry [#permalink]  06 Nov 2006, 07:02
trivikram wrote:
kidderek wrote:
Why is B insuff?

If angle BCO=40, angle CBO=40 b/c triangle BCO is isosceles, with legs BO=CO (each is a radius of the semicircle)

If angle CBO=40, then angle ABO=140

triangle ABO=isosceles with AB=BO

therefore, angle BAO=BOA=20

Yep...B should be enough...

Anyone else?

OA is D
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(1) is sufficient

Triangle BCO is isoceles so angle OBC = angle BCO. Call this t. Then Angle BOC = 180 - 2t.

180 = Angle BOA + angle BOC + angle COD
= Angle BOA + 180 - 2t + 60

=> angle BOA = 2t - 60

Further, since angle OBC = t then angle OBA = 180 - t.

Triangle ABO is isoceles so angle BAO = angle BOA = 2t - 60

Finally, 180 = angle BAO + angle BOA + angle OBA
= 2t - 60 + 2t -60 + 180 - t

So t = 40

angle BAO = angle BOA = 20.

(2) is sufficient (see Kidderek's fine proof above)
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Re: GMATPrep geometry [#permalink]  06 Nov 2006, 09:00
i solved to get choice D
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joey,

i can tell by your posts that you are very good in quant. you actually post explanations rather than restating the already posted OA.

1 question, at what point did you know that (1) is sufficient? Was it when you saw the information given, or did you have to play around with the diagram before it clicked in your head that it is SUFF?
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kidderek wrote:
joey,

i can tell by your posts that you are very good in quant. you actually post explanations rather than restating the already posted OA.

1 question, at what point did you know that (1) is sufficient? Was it when you saw the information given, or did you have to play around with the diagram before it clicked in your head that it is SUFF?

Thanks. It's hard to answer exactly. When I look at problems like this, I have a feel for how much structure there is in the problem and how much info I need. In this problem, I would have bet at very impressive odds that (1) was sufficient immediately.
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I also got this question when I did my test prep, and the OA is D.

I got B orginally becuase I brought in the information from A.

What overall math score did you get?
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Never took GMAT's. I'm a quant sitting out a non-compete trying to stay sharp. This seems like a good activity...
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lfox2 wrote:
I also got this question when I did my test prep, and the OA is D.

I got B orginally becuase I brought in the information from A.

What overall math score did you get?

If the question was for me, I also answered this question as B, b/c I couldn't do much with statement 1. I got 10 wrong on quant and got a 47, I believe (need to double check). Oddly, I had 18 DS questions instead of the normal 15 DS, which I think lowered my score.

I stink at DS, my hit rate fluctuates from 50% to 80%
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kidderek wrote:
joey,

i can tell by your posts that you are very good in quant. you actually post explanations rather than restating the already posted OA.

1 question, at what point did you know that (1) is sufficient? Was it when you saw the information given, or did you have to play around with the diagram before it clicked in your head that it is SUFF?

Good question kidderek. In fact I picked out the choice 2 quite easily using the same logic as you have used.

But at first glance wasn't yielding me the result. It was only when I did the calculation that I realized 1 is sufficient as well. I am pretty good in Geometry, but I just couldn't believe GMAT would need so much calculation..

There must be a shorter, quicker way of calculating this.
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Remember that you don't have to calculate the answer; you just need to know that you can. Thus, if you just start labeling everything in terms of t, you will find that eventually you have an equation that amounts to solve for t. That makes it sufficient and go on.
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This question has been done a few times before - some interesting alternative explanations if you do search:

One example:
http://www.gmatclub.com/phpbb/viewtopic ... highlight=
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Alternative way of solving in 1)

Triangle COD is equilateral - angles equalling 60

Call angle BAO - x Therefore angle BOA is also x

Angle ABO is therefore 180 - 2x

Therefore 2x = angle OBC because angles ABO and OBC = 180

We know triangle OBC is isosceles so angle BCO also 2x

From larger triangle ACD:

BAO + (BCO+60) + 60 = 180 ---> x + (x+60) + 60 = 180

x = 20

This is not my working but that of giddi77 - I found it easier to follow. He's also provided a diagram on the link I've posted above.
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St1 suff
st2 is suff
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