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by sanju09 » Mon Sep 20, 2010 3:04 am
girishbtg wrote:Image

We have AB = OC = OB = r, the radius of circle in question. What is ∠BAO?

≡ ∠BAO = ∠BOA = let x =?

∴ ∠CBO = ∠BCO = 2 x.

[1] If ∠COD = 60º, then ∠COA = 120º

Or, ∠COB + ∠BOA = 120º

Or, we have a linear in x, sufficient

[2] If ∠BCO = 2 x = 40º, then x = 20º, sufficient


[spoiler]D[/spoiler]
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by girishbtg » Mon Sep 20, 2010 3:42 am
sanju09 wrote:
girishbtg wrote:Image

We have AB = OC = OB = r, the radius of circle in question. What is ∠BAO?

≡ ∠BAO = ∠BOA = let x =?

∴ ∠CBO = ∠BCO = 2 x.

[1] If ∠COD = 60º, then ∠COA = 120º

Or, ∠COB + ∠BOA = 120º

Or, we have a linear in x, sufficient

[2] If ∠BCO = 2 x = 40º, then x = 20º, sufficient


[spoiler]D[/spoiler]

Thanks for Responding...

but still am not able to find out that how A ( i.e. eq 1 ) is sufficient in itself... Plz elaborate

Thanks!
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by sanju09 » Mon Sep 20, 2010 4:06 am
girishbtg wrote:
sanju09 wrote:
girishbtg wrote:Image

We have AB = OC = OB = r, the radius of circle in question. What is ∠BAO?

≡ ∠BAO = ∠BOA = let x =?

∴ ∠CBO = ∠BCO = 2 x.

[1] If ∠COD = 60º, then ∠COA = 120º

Or, ∠COB + ∠BOA = 120º

Or, ∠COB + ∠BOA = 120º

Or, we have a linear in x, sufficient

[2] If ∠BCO = 2 x = 40º, then x = 20º, sufficient


[spoiler]D[/spoiler]

Thanks for Responding...

but still am not able to find out that how A ( i.e. eq 1 ) is sufficient in itself... Plz elaborate

Thanks!

[1] If ∠COD = 60º, then ∠COA = 120º

Or, ∠COB + ∠BOA = 120º

Or, 180º - 4 x + x = 120º

Or, x = 20º. Hence, sufficient
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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by girishbtg » Mon Sep 20, 2010 4:14 am
sanju09 wrote:
girishbtg wrote:
sanju09 wrote:
girishbtg wrote:Image

We have AB = OC = OB = r, the radius of circle in question. What is ∠BAO?

≡ ∠BAO = ∠BOA = let x =?

∴ ∠CBO = ∠BCO = 2 x.

[1] If ∠COD = 60º, then ∠COA = 120º

Or, ∠COB + ∠BOA = 120º

Or, ∠COB + ∠BOA = 120º

Or, we have a linear in x, sufficient

[2] If ∠BCO = 2 x = 40º, then x = 20º, sufficient


[spoiler]D[/spoiler]

Thanks for Responding...

but still am not able to find out that how A ( i.e. eq 1 ) is sufficient in itself... Plz elaborate

Thanks!

[1] If ∠COD = 60º, then ∠COA = 120º

Or, ∠COB + ∠BOA = 120º

Or, 180º - 4 x + x = 120º

Or, x = 20º. Hence, sufficient

Great...!

Thanks!
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by GMATGuruNY » Mon Sep 20, 2010 4:18 am
girishbtg wrote:Image
When you want to see how the angles in a figure affect each other, plug in twice. The attached .pdf shows two sets of angle measurements that satisfy the requirements of the figure. In each case, we can see that COD:BAO = 3:1 and that BCO:BAO = 2:1.

Statement 1:
If COD = 60, then 60:BAO = 3:1, and BAO = 20. Sufficient.

Statement 2:
If BCO = 40, then 40:BAO = 2:1, and BAO = 20. Sufficient.

The correct answer is D.
Attachments
Relationships_between_angles.pdf
(36.41 KiB) Downloaded 105 times
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