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26 Sep 2022, 12:13
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
81% (00:44) correct
19%
(01:13)
wrong
based on 73
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, what is the value of a?
(1) c + d = 146
(2) 2b + c + d = 214
Attachment:
2022-09-26_23-11-33.png [ 5.09 KiB | Viewed 1622 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:
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27 Sep 2022, 20:25
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Bunuel
\(a=180-b\)
\(b+c+d=180\)
(1) c + d = 146
So b=180-(c+d)=180-146=34
a=c+d=180-b=146
Sufficient
(2) 2b + c + d = 214
b+b+c+d=214
b+180=214
b=214-180=34
a=180-b=180-34=146
Sufficient
D
28 Sep 2022, 04:00
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Bunuel
Solution:
Pre-Analysis:
- From the figure above, we can say
- \(b+c+d=180\)....(angle of a triagle)
- \(a+b=180\) or \(a=180-b\).....(straight angle)
- \(a=c+d\).....(exterior angle of a triangle is equal to sum of two opposite interior angles)
Statement 1: \(c + d = 146\)
- We know from pre-analysis that \(a=c+d\)
- Thus, we can find the value of \(a=c+d=146\)
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: \(2b + c + d = 214\)
- We know from pre-analysis that \(b+c+d=180\)
- Thus, we can write \(2b+c+d=b+b+c+d=b+180=214\) or \(b=214-180=34\)
- Now that we know the value of b, we can get the value of a as \(a=180-b=180-34=146\)
- Thus, statement 2 alone is also sufficient
Hence the right answer is Option D
