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26 Nov 2019, 01:00
Kudos
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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:
35%
(medium)
Question Stats:
69% (01:29) correct
31%
(01:53)
wrong
based on 100
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In the figure above, AC is tangent to circle B at point A. What is the area of the shaded region?
(1) The area of the circle is 49 in^2.
(2) AB:BC = 1:2
Are You Up For the Challenge: 700 Level Questions
Attachment:
CircleShadegee.jpg [ 12.11 KiB | Viewed 5199 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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Data Sufficiency Forum
26 Nov 2019, 03:37
Kudos
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Area of shaded region = Area(ABC)- sector of the circle
hence, we need radius and angle B or C
Statement 1- it gives us radius, We don't know angle B or C
Insufficient'
Statement 2- it gives us angle B and C. we have no clue about radius.
Insufficient
Combining both equations, we will have radius and angle B or C
Sufficient
hence, we need radius and angle B or C
Statement 1- it gives us radius, We don't know angle B or C
Insufficient'
Statement 2- it gives us angle B and C. we have no clue about radius.
Insufficient
Combining both equations, we will have radius and angle B or C
Sufficient
Bunuel
26 Nov 2019, 04:30
Kudos
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Bunuel
AC is tang to Circle B, then BAC is a right triangle;
Shaded region = Sector area - Triangle area.
(1) The area of the circle is 49 in^2. insufic
\(πr^2=49…r^2=49/π…r=\sqrt{49/π}\)
(2) AB:BC = 1:2 insufic
AB:BC=1:2
AC: \(4=1-x^2…x=\sqrt{3}\)
AB:AC:BC=1x:x√3:2x=30:60:90
(1&2) sufic
\(AB=r\)
\(T_{area}=r(r√3)/2\)
\(Sector_{area}=49*60/360\)
\(Shaded_{area}=T_{area}-Sector_{area}\)
Ans (C)
