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.
The two statements cannot contradict each other.
It must be POSSIBLE for both statements to be true AT THE SAME TIME.
If COD=60 and BCO=40, then the angle measurements are as follows:
The combination above satisfies all of the rules of geometry.
The sum of the angles inside each triangle is 180.
The sum of any angles that form a straight line is 180.
In this case, BAO=20.
Now we need to determine whether it's possible for one statement to be true WITHOUT the other.
Statement 1 alone: COD=60
Let BCO=50, implying the following combination of angles:
The combination above is not valid: ABO+OBC = 100+50 = 150, but the sum of these angles must be 180.
Thus, if COD=60, then IT MUST BE TRUE that BCO=40, implying that BAO=20 (as we saw in the first drawing).
SUFFICIENT.
Statement 2 alone: BCO=40
Let COD=50, implying the following combination of angles:
The combination above is not valid: ABO+OBC = 120+40 = 160, but the sum of these angles must be 180.
Thus, if BCO=40, then IT MUST BE TRUE that COD=60, implying that BAO=20 (as we saw in the first drawing).
SUFFICIENT.
The correct answer is
D.
This problem illustrates how the GMAT is not really a math test but a REASONING test.
By taking advantage of how the test is constructed -- that it must be possible for both statements to be true at the same time -- we can quickly see that it is NOT possible for one statement to be true WITHOUT the other.
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