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27 May 2018, 10:02
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (02:36) correct
38%
(02:27)
wrong
based on 125
sessions
History
Date
Time
Result
Not Attempted Yet
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 [ 23.16 KiB | Viewed 3531 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
28 May 2018, 06:22
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Bunuel
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)
28 May 2018, 07:45
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Solution
Given:
In the given figure,
- • Angle BAD = 60°
• ABCD is a parallelogram
• Line BC bisects line AE, i.e. AB = BE
To find:
- • Length of the side EC
Analysing Statement 1
- • As per the information provided in Statement 1, DC = 12
- o From this, we can say AB = 12, as ABCD is a parallelogram
o We can also say BE = 12, as AB = BE
Hence, statement 1 is not sufficient to answer
Analysing Statement 2
- • As per the information provided in Statement 2, BC = 12
- o From this, we can say AD = 12, as ABCD is a parallelogram
Hence, statement 2 is not sufficient to answer
Combining Both Statements
If we combine the information available in both the statements, we can say,
- • AB = BE = DC = BC = AD = 12
• Angle BAD = 60°
- o Therefore, angle ABC = 180° - 60° = 120°
o Hence, angle EBC = 60°
- o Therefore, we can write 60° + x + x = 180°
Or, x = 60°
• Hence, EC = 12
Hence, the correct answer is option C.
Answer: C
