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# In the figure shown, point O is the center of the circle and points B,

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In the figure shown, point O is the center of the circle and points B,  [#permalink]

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21 Apr 2015, 04:49
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Difficulty:

85% (hard)

Question Stats:

50% (02:22) correct 50% (02:57) wrong based on 167 sessions

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In the figure shown, point O is the center of the circle and points B, C, and D lie on the circle. If the 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

Kudos for a correct solution.

Attachment:

GMAT1.jpg [ 17.97 KiB | Viewed 4698 times ]

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Re: In the figure shown, point O is the center of the circle and points B,  [#permalink]

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21 Apr 2015, 07:38
1
Bunuel wrote:
Attachment:
GMAT1.jpg
In the figure shown, point O is the center of the circle and points B, C, and D lie on the circle. If the 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

Kudos for a correct solution.

1) Insufficient
2) We know that BO=CO because they are radiuses. So we know that angle OCB equal to angle BCO and equal to 40 degree
angle ABO equal 180 - CBO = 180 - 40 = 140 degrees
AB = OC = BO so triangle ABO isosceles, so angles BAO and BOA are equal and equal to 180 - ABO = 180 - 140 = 40 / 2 = 20 degrees
Sufficient.

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Re: In the figure shown, point O is the center of the circle and points B,  [#permalink]

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21 Apr 2015, 20:21
1
A) If COD = 60, then we would end COD as equilateral triangle. -- Insufficient.

B) If BCO = 40, then In BCO OC = OB(Radius) Thus angles CBO= OCB = 40.
We know that angle in a straight line = 180. Thus ABC line make 180. Thus ABO = 140.
Triangle ABO AB = OB , thus angle BAO = BOA . Thus B alone is sufficient to find the angle BAO .

B Alone is sufficient
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Re: In the figure shown, point O is the center of the circle and points B,  [#permalink]

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22 Apr 2015, 01:13
1
Bunuel wrote:
Attachment:
GMAT1.jpg
In the figure shown, point O is the center of the circle and points B, C, and D lie on the circle. If the 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

Kudos for a correct solution.

Hello,

Here is a detailed explanation of how I approached it:

Step 1: Lets mark all lines that will be equal based on the question stem

• AB =OB=OC [OB and OC are radii lines]
• Applying similar triangle theories, we know that angle opposite to equal sides will be equal. This gives us:
o Angle CBO = angle BCO --- i
o Angle BOA = angle BAO---ii

Now let’s move to the statements

Statement 1: If angle COD is 60 degrees then angle COA = 180-60=120.

But we don’t know how is this 120 degrees split between angle COB and angle BOA.

So, insufficient

Statement 2: Angle BCO is 40 degrees

Using i we know that angle CBO is 40 too.

Angle ABO is 180-40 = 140 degrees [ they are on a straight line]

Using ii we know that the remaining 40 degrees should be equally divided between angle BOA and angle BAO. i.e. 20 degree each.

Hence statement 2 is sufficient --> B

Thanks,
aimtoteach

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Re: In the figure shown, point O is the center of the circle and points B,  [#permalink]

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22 Apr 2015, 01:56
1
D

Solution in the attached file
Attachments

Circle.pdf [115.74 KiB]

Intern
Joined: 06 Aug 2014
Posts: 17
Re: In the figure shown, point O is the center of the circle and points B,  [#permalink]

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22 Apr 2015, 02:04
2
1

Statement-1 is sufficient
<COD = 60 so < COA = 120

Now BO=OC => <OCB = < CBO let it be 2X

<CBO is exterior angle for <BAO and <BOA
=> < CBO = <BAO + <BOA
=> <BAO = <BOA = X

Since <OCB = < CBQ = 2X
=> <COB = 180 - 4X

Now <COB+<BOA = 120
=> 180-4X+X = 120
=> X = 20
=> <BAO = 20
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Re: In the figure shown, point O is the center of the circle and points B,  [#permalink]

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22 Apr 2015, 10:23
Yes.. The Answer is D. But really a good brainer.

Bunuel wrote:
Attachment:
GMAT1.jpg
In the figure shown, point O is the center of the circle and points B, C, and D lie on the circle. If the 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

Kudos for a correct solution.

_________________

Kudos to you, for helping me with some KUDOS.

Math Expert
Joined: 02 Sep 2009
Posts: 52971
Re: In the figure shown, point O is the center of the circle and points B,  [#permalink]

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27 Apr 2015, 02:24
3
1
Bunuel wrote:

In the figure shown, point O is the center of the circle and points B, C, and D lie on the circle. If the 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

Kudos for a correct solution.

Attachment:
The attachment GMAT1.jpg is no longer available

VERITAS PREP OFFICIAL SOLUTION:

That is a complicated-looking figure. Your instinct might be that you don’t have time to draw it, but these kinds of questions will be designed specifically to thwart our intuition if we attempt to do too much work in our heads. So the first thing to do is draw the figure on our scratch pad, and mark the relationships we’re given. We’re told that segment CO is equal to AB, so we’ll designate that relationship. We’ll also call angle BAO, which we’re asked about, ‘x.’ Now we have the following:
Attachment:

GMAT2.jpg [ 18.14 KiB | Viewed 3788 times ]

Fight the impulse to jump to the statements now. In a harder question like this, we’ll benefit from taking more time to derive additional relationships from the question stem. Psychologically, this is often a struggle for test-takers. You’re conscious of your time constraint. You want to work quickly. The trick is to trust that this pre-statement investment of time will allow you to evaluate the information provided in the statements more efficiently, ultimately saving time.

Now the name of the game is to try to label as much of this figure as we can without introducing a new variable. Notice that segments CO and BO are both radii of the circle, so we know those are equal. Our diagram now looks like this:
Attachment:

GMAT3.jpg [ 18.4 KiB | Viewed 3787 times ]

Next, look at triangle ABO. Notice that segments AB and BO are equal. If angles opposite equal angles are equal to each other, we can then designate angle AOB as ‘x’ because it must be equal to angle BAO, as those two angles are opposite sides that are of equal length. Moreover, if the three interior angles of a triangle will sum to 180, the remaining angle, ABO, can be designated 180-2x. This gives us the following.
Attachment:

GMAT4.jpg [ 18.91 KiB | Viewed 3784 times ]

No reason to stop here. Notice that angles ABO and CBO lie on a line. Angles that lie on a line must sum to 180. If angle ABO is 180-2x, then angle CBO must be 2x. Now we have this:
Attachment:

GMAT5.jpg [ 19.62 KiB | Viewed 3781 times ]

Analyzing triangle CBO, we see that sides BO and CO are equal, meaning that the angles opposite those sides must be equal. So now we can label angle BCO as ‘2x.’ If angles CBO and BOC sum to 4x, the remaining angle, BOC, must then be 180-4x, so that the interior angles of the triangle will sum to 180.
Attachment:

GMAT6.jpg [ 19.59 KiB | Viewed 3785 times ]

We’ve got enough at this point that we can very quickly evaluate our statements, However, there is one last interesting relationship. Notice that angle COD is an exterior angle of triangle CAO. An exterior angle, by definition, must be equal to the sum of the two remote interior angles. So, in this case, Angle COD is equal to the sum of angles BCO and BAO. Therefore COD = 2x + x = 3x, which I’ve circled in the figure. (Triangle CAO is outlined in blue in the figure below to more clearly demarcate the exterior angle.)

Attachment:

GMAT7.jpg [ 20.77 KiB | Viewed 3786 times ]

That’s a lot of work. Determining all of these relationships will likely take close to two minutes. But watch how quickly we can evaluate our statements if we’ve done all of this preemptive groundwork:

Statement 1: Angle COD = 60. We’ve designated angle COD as 3x, so 3x = 60. Clearly we can solve for x. Sufficient. Eliminate BCE.

Statement 2: Angle BCO = 40. We’ve designated angle BCO as 2x, so 2x = 40. Clearly we can solve for x. Sufficient. Answer is D.

Notice, all of the heavy lifting for this question came before we even so much as glanced at our statements.

Takeaway: For a challenging Data Sufficiency question in which you’re given a lot of information in the question stem, the best approach is to spend some time taming the complexity of the problem before examining the statements. When you work out these relationships, try to minimize the number of variables you use when doing so, as this will simplify your calculations once you’re ready to go to the statements. Most importantly, don’t do too much work in your head. There’s no need to rely on the limited bandwidth of your working memory if you have the option of putting everything into a concrete form on your scratch pad.
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Re: In the figure shown, point O is the center of the circle and points B,  [#permalink]

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27 Apr 2015, 09:10
1

I got this one wrong - interestingly, I knew all the properies but got it wrong simply because I jumped straight to the statements. To be honest, if this question comes after the 20th question in GMAT - I dont know how will I be able to control the urge to jump to statements!

Bunuel wrote:
Bunuel wrote:

In the figure shown, point O is the center of the circle and points B, C, and D lie on the circle. If the 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

Kudos for a correct solution.

Attachment:
GMAT1.jpg

VERITAS PREP OFFICIAL SOLUTION:

That is a complicated-looking figure. Your instinct might be that you don’t have time to draw it, but these kinds of questions will be designed specifically to thwart our intuition if we attempt to do too much work in our heads. So the first thing to do is draw the figure on our scratch pad, and mark the relationships we’re given. We’re told that segment CO is equal to AB, so we’ll designate that relationship. We’ll also call angle BAO, which we’re asked about, ‘x.’ Now we have the following:
Attachment:
GMAT2.jpg

Fight the impulse to jump to the statements now. In a harder question like this, we’ll benefit from taking more time to derive additional relationships from the question stem. Psychologically, this is often a struggle for test-takers. You’re conscious of your time constraint. You want to work quickly. The trick is to trust that this pre-statement investment of time will allow you to evaluate the information provided in the statements more efficiently, ultimately saving time.

Now the name of the game is to try to label as much of this figure as we can without introducing a new variable. Notice that segments CO and BO are both radii of the circle, so we know those are equal. Our diagram now looks like this:
Attachment:
GMAT3.jpg

Next, look at triangle ABO. Notice that segments AB and BO are equal. If angles opposite equal angles are equal to each other, we can then designate angle AOB as ‘x’ because it must be equal to angle BAO, as those two angles are opposite sides that are of equal length. Moreover, if the three interior angles of a triangle will sum to 180, the remaining angle, ABO, can be designated 180-2x. This gives us the following.
Attachment:
GMAT4.jpg

No reason to stop here. Notice that angles ABO and CBO lie on a line. Angles that lie on a line must sum to 180. If angle ABO is 180-2x, then angle CBO must be 2x. Now we have this:
Attachment:
GMAT5.jpg

Analyzing triangle CBO, we see that sides BO and CO are equal, meaning that the angles opposite those sides must be equal. So now we can label angle BCO as ‘2x.’ If angles CBO and BOC sum to 4x, the remaining angle, BOC, must then be 180-4x, so that the interior angles of the triangle will sum to 180.
Attachment:
GMAT6.jpg

We’ve got enough at this point that we can very quickly evaluate our statements, However, there is one last interesting relationship. Notice that angle COD is an exterior angle of triangle CAO. An exterior angle, by definition, must be equal to the sum of the two remote interior angles. So, in this case, Angle COD is equal to the sum of angles BCO and BAO. Therefore COD = 2x + x = 3x, which I’ve circled in the figure. (Triangle CAO is outlined in blue in the figure below to more clearly demarcate the exterior angle.)

Attachment:
GMAT7.jpg

That’s a lot of work. Determining all of these relationships will likely take close to two minutes. But watch how quickly we can evaluate our statements if we’ve done all of this preemptive groundwork:

Statement 1: Angle COD = 60. We’ve designated angle COD as 3x, so 3x = 60. Clearly we can solve for x. Sufficient. Eliminate BCE.

Statement 2: Angle BCO = 40. We’ve designated angle BCO as 2x, so 2x = 40. Clearly we can solve for x. Sufficient. Answer is D.

Notice, all of the heavy lifting for this question came before we even so much as glanced at our statements.

Takeaway: For a challenging Data Sufficiency question in which you’re given a lot of information in the question stem, the best approach is to spend some time taming the complexity of the problem before examining the statements. When you work out these relationships, try to minimize the number of variables you use when doing so, as this will simplify your calculations once you’re ready to go to the statements. Most importantly, don’t do too much work in your head. There’s no need to rely on the limited bandwidth of your working memory if you have the option of putting everything into a concrete form on your scratch pad.

_________________

Thanks,
aimtoteach

~~~~~~~~~~~~~~~~~

Please give Kudos if you find this post useful.

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Re: In the figure shown, point O is the center of the circle and points B,  [#permalink]

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13 Apr 2018, 02:49
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Re: In the figure shown, point O is the center of the circle and points B,   [#permalink] 13 Apr 2018, 02:49
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