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12 Oct 2022, 01:30
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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:
5%
(low)
Question Stats:
96% (00:33) correct
4%
(00:55)
wrong
based on 120
sessions
History
Date
Time
Result
Not Attempted Yet
In triangle ABC shown above, what is the value of x ?
(1) y = 80
(2) AB = BC
Attachment:
2022-09-23_16-42-37.png [ 15 KiB | Viewed 3538 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
06 Mar 2023, 17:07
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Since the sum of the angles of a triangle is \(180\) degrees, we know that: \(x = 180 - y - z\), where \(z\) is the angle opposite to \(AC\).
(I) \(y = 80\)
With this statement, we have \(x = 100 - z\). This is not sufficient, since \((x,z) = (50,50)\) would be an option, as well as \((x,z) = (60,40)\). In fact, there are infinite solutions to this system.
I is not sufficient
(II) \(AB = BC\)
With this statement, we know the angles opposing \(AB\) and \(BC\) should be the same, which means \(x = y\). So, using our initial equation: \(x = 180 - x - z \Rightarrow 2x = 180 - z \Rightarrow x = \frac{180-z}{2}\). There are infinite solutions to this system.
II is not sufficient
(I + II)
With statement II, we know \(x = y\). Since \(y = 80\) with statement I, both statements, when combined, are sufficient.
I + II is sufficient
Answer: C
(I) \(y = 80\)
With this statement, we have \(x = 100 - z\). This is not sufficient, since \((x,z) = (50,50)\) would be an option, as well as \((x,z) = (60,40)\). In fact, there are infinite solutions to this system.
I is not sufficient
(II) \(AB = BC\)
With this statement, we know the angles opposing \(AB\) and \(BC\) should be the same, which means \(x = y\). So, using our initial equation: \(x = 180 - x - z \Rightarrow 2x = 180 - z \Rightarrow x = \frac{180-z}{2}\). There are infinite solutions to this system.
II is not sufficient
(I + II)
With statement II, we know \(x = y\). Since \(y = 80\) with statement I, both statements, when combined, are sufficient.
I + II is sufficient
Answer: C
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