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11 Oct 2018, 01:35
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C
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Difficulty:
15%
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Question Stats:
80% (00:45) correct
20%
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[Math Revolution GMAT math practice question]
11.11.png [ 6.48 KiB | Viewed 2992 times ]
The above figure shows a sector of a circle. What is the area of the sector?
\(1) x = 120^o.\)
\(2) AB=6√3.\)
Attachment:
11.11.png [ 6.48 KiB | Viewed 2992 times ]
The above figure shows a sector of a circle. What is the area of the sector?
\(1) x = 120^o.\)
\(2) AB=6√3.\)
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
11 Oct 2018, 01:41
Kudos
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From statement 1:
Area of a sector is given by pi*\(r^2\)*\(\frac{120}{360}\)
only angle is given. no info about the radius.
Hence insufficient.
From statement 2:
Length of the Arc is given. No info about the angle.
Insufficient.
Combining both:
The area can be found.
C is the answer.
Area of a sector is given by pi*\(r^2\)*\(\frac{120}{360}\)
only angle is given. no info about the radius.
Hence insufficient.
From statement 2:
Length of the Arc is given. No info about the angle.
Insufficient.
Combining both:
The area can be found.
C is the answer.
11 Oct 2018, 02:14
Kudos
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MathRevolution
Statement 1: \(x= 120^0\). Clearly NOT sufficient . This information can be useful if we know the total area or part of the area of the circle.
Statement 2: AB =6√3 . Using this information , all we can do is to find out the total area. AB is basically diameter here. As we don't know the ration of % of this sector , This pieces of information alone is useless. NOT sufficient.
Combining both statements :
we have total area from statement 2 and the % from statement 1. Sufficient.
The best answer is C.
11 Oct 2018, 07:32
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MathRevolution
(We assume - as part of the definition of a sector a circle - that the "origin" of the angle x shown in the figure is the center of the circle.)
The variable R will denote the radius of the circle. All angles are measured in degrees.
\(? = \frac{{x\,}}{{360\,}}\left( {\pi {R^{\,2}}} \right)\)
\(x = 120\,\,\,\left( {{\text{both}}\,\,{\text{figures}}} \right)\)
\(AB = 6\sqrt 3 \,\,\,\left( {{\text{both}}\,\,{\text{figures}}} \right)\)
\(x = 90\,\,\,\mathop {\,\,\, \Rightarrow \,\,\,\,}\limits^{L\,,\,L\,,\,L\sqrt 2 } \,\,\,R\sqrt 2 = 6\sqrt 3 \,\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,\frac{{\sqrt 2 }}{2}\,} \,\,\,\,\,R = 3\sqrt 6 \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,?\,\,\, = \,\,\,\frac{1}{4}\,\left( {\pi \, \cdot 9 \cdot 6} \right)\)
\(x = 120\,\,\,\mathop \Rightarrow \limits_{\left( * \right)}^{30\,,\,60\,,\,90\,\,} \,\,\,\,?\,\,\, = \,\,\,\frac{1}{3}\,\left( {\pi \, \cdot 36} \right)\,\,\, = 12\pi \,\,\, \ne \,\,\,\,\frac{1}{4}\,\left( {\pi \, \cdot 9 \cdot 6} \right)\,\,\,\,\,\,\)
\(\left( * \right)\,\,30\,,\,60\,,\,90\,\,\,\, \Rightarrow \,\,\,\,\left\{ \begin{gathered}\\
\,L\sqrt 3 \,\,\, = \,\,\frac{{6\sqrt 3 }}{2} \hfill \\\\
\,2L = R \hfill \\ \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,R = 6\)
\(\left( {1 + 2} \right)\,\,\,?\,\, = \,\,12\pi \,\,\,\left( {{\text{shown}}\,\,{\text{above}}} \right)\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
