Bunuel wrote:
In the figure shown, if the measure of angle BAD is 60 degrees, ABCD is a parallelogram, and line BC bisects line AE, what is the length of side EC?
(1) The length of DC is 12.
(2) The length of BC is 12.
Attachment:
screen_shot_2011_01_06_at_12.27.16_pm.png
From the question stem, we can deduce the following information
1. In a parallelogram, the opposite sides are equal. Here, AB = CD and BC = AD.
2. Opposite angles are supplementary - angle CBA = 120.
3. CBE + CBA = 180 -> CBE = 180 - 120 = 60 degree
1. AB = 12. Since the line bisects AE, EB = BA = 12.
We have no idea about the length of BC and we can't come to a conclusion about
the length of EC.
(Insufficient)2. Knowing the length of BC alone is not enough to come to a conclusion about the
length of EC.
(Insufficient)Combining the information present in both the statements and the question stem,
we know that the triangle EBC is equilateral and EC = 12
(Sufficient - Option C)
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