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## Any thoughts how 1 could work alone? Thank you

tagged by: Brent@GMATPrepNow

This topic has 1 expert reply and 0 member replies
Ehab Salah Newbie | Next Rank: 10 Posts
Joined
17 Jan 2017
Posted:
2 messages

#### Any thoughts how 1 could work alone? Thank you

Sat Nov 04, 2017 5:51 am



### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11292 messages
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Tue Nov 07, 2017 8:47 am
Quote:

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 60Âº
(2) The degree measure of angle BCO is 40Âº
Target question: What is the degree measure of âˆ 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 60Âº
So, we have the following:

Since the radii must have equal lengths, we can see that OB = OC

So, âˆ†ABO is an isosceles triangle.

If we let âˆ BAO = x degrees, then we can use the facts that âˆ†ABO is isosceles and that angles must add to 180Âº to get the following:

Since angles on a LINE must add to 180Âº, we know that âˆ OBC = 2x

Now, we can use the facts that âˆ†BCO is isosceles and that the angles must add to 180Âº 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, âˆ BAO = 20Âº
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The degree measure of angle BCO is 40Âº
So, we have the following:

Since the radii must have equal lengths, we can see that OB = OC

So, âˆ†BCO is an isosceles triangle, which means OBC is also 40Âº

Since angles on a line must add to 180 degrees, âˆ ABO = 140Âº

Finally, since âˆ†ABO is an isosceles triangle, the other two angles must each be 20Âº

As we can see, âˆ BAO = 20Âº
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
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