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What is the degree measure of angle BAO?
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Brent@GMATPrepNow
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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 sement OC, what is the degree measure of angle BAO?
(1) The degree measure of angle COD is 60º
(2) The degree measure of angle BCO is 40º
Target question: What is the degree measure of ∠BAO?
Given: The length of line segment AB is equal to the length of line sement OC
Statement 1: The degree measure of angle COD is 60º
So, we have the following:
Since the radii must have equal lengths, we can see that OB = OC
So, ∆ABO is an isosceles triangle.
If we let ∠BAO = x degrees, then we can use the facts that ∆ABO is isosceles and that angles must add to 180º to get the following:
Since angles on a LINE must add to 180º, we know that ∠OBC = 2x
Now, we can use the facts that ∆BCO is isosceles and that the angles must add to 180º to get the following:
Finally, we can see that the 3 angles with blue circles around them are on a line.
So, they must add to 180 degrees.
We get: x + (180-4x) + 60 = 180
Simplify: 240 - 3x = 180
Solve to get: x = 20
In other words, ∠BAO = 20º
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The degree measure of angle BCO is 40º
So, we have the following:
Since the radii must have equal lengths, we can see that OB = OC
So, ∆BCO is an isosceles triangle, which means OBC is also 40º
Since angles on a line must add to 180 degrees, ∠ABO = 140º
Finally, since ∆ABO is an isosceles triangle, the other two angles must each be 20º
As we can see, ∠BAO = 20º
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
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GMATGuruNY
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It is given that AB=OC.
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 sement 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.
Since OC and OB are both radii, OC=OB.
Thus:
EVALUATE THE EASIER STATEMENT FIRST.
Since statement 2 gives information about one of the equal angles, start with statement 2.
Statement 2: The degree measure of angle BCO is 40.
The result is the following combination of angles:
Thus, angle BAO = 20.
SUFFICIENT.
Statement 1: The degree measure of angle COD is 60.
In the combination of angles yielded by statement 2, angle COD = 60.
Thus, statement 1 implies the same combination of angles as does statement 2.
SUFFICIENT.
The correct answer is D.
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Turksonaaron
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Hi MitchGMATGuruNY wrote:It is given that AB=OC.
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 sement 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.
Since OC and OB are both radii, OC=OB.
Thus:
EVALUATE THE EASIER STATEMENT FIRST.
Since statement 2 gives information about one of the equal angles, start with statement 2.
Statement 2: The degree measure of angle BCO is 40.
The result is the following combination of angles:
Thus, angle BAO = 20.
SUFFICIENT.
Statement 1: The degree measure of angle COD is 60.
In the combination of angles yielded by statement 2, angle COD = 60.
Thus, statement 1 implies the same combination of angles as does statement 2.
SUFFICIENT.
The correct answer is D.
I get the fact that the answer is D. I was looking at your solution to get a faster route to solve it. However, I don't really understand your explanation of statement 1 which makes it sufficient.
Thanks
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GMATGuruNY
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Statement 2: ∠BCO = 40ºTurksonaaron wrote:Hi Mitch
I get the fact that the answer is D. I was looking at your solution to get a faster route to solve it. However, I don't really understand your explanation of statement 1 which makes it sufficient.
Thanks
Here, the following figure is yielded:
In the figure above, ∠BAO = 20º.
SUFFICIENT.
Statement 1: ∠COD = 60º
The figure yielded by Statement 2 indicates the following:
If ∠BCO = 40º, then ∠COD = 60º.
Strategy:
Test whether it's possible for ∠BCO to be less than or greater than 40º.
Case 2: ∠BCO = 30º
Here, the following figure is yielded:
In this case, ∠COD is LESS THAN 60º.
Case 3: ∠BCO = 50º
Here, the following figure is yielded:
In this case, ∠COD is GREATER THAN 60º.
If ∠BCO is less than or greater than 40º, then ∠COD ≠60º.
Implication:
To satisfy the constraint that COD = 60º, it must be true that ∠BCO = 40º, as indicated in Statement 2.
In other words, Statement 1 implies the SAME COMBINATION OF ANGLES as Statement 2.
Thus, ∠BAO = 20º.
SUFFICIENT.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Turksonaaron
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Alright. Thank youGMATGuruNY wrote:Statement 2: ∠BCO = 40ºTurksonaaron wrote:Hi Mitch
I get the fact that the answer is D. I was looking at your solution to get a faster route to solve it. However, I don't really understand your explanation of statement 1 which makes it sufficient.
Thanks
Here, the following figure is yielded:
In the figure above, ∠BAO = 20º.
SUFFICIENT.
Statement 1: ∠COD = 60º
The figure yielded by Statement 2 indicates the following:
If ∠BCO = 40º, then ∠COD = 60º.
Strategy:
Test whether it's possible for ∠BCO to be less than or greater than 40º.
Case 2: ∠BCO = 30º
Here, the following figure is yielded:
In this case, ∠COD is LESS THAN 60º.
Case 3: ∠BCO = 50º
Here, the following figure is yielded:
In this case, ∠COD is GREATER THAN 60º.
If ∠BCO is less than or greater than 40º, then ∠COD ≠60º.
Implication:
To satisfy the constraint that COD = 60º, it must be true that ∠BCO = 40º, as indicated in Statement 2.
In other words, Statement 1 implies the SAME COMBINATION OF ANGLES as Statement 2.
Thus, ∠BAO = 20º.
SUFFICIENT.
The correct answer is D.
