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Difficulty:
25%
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Question Stats:
77% (01:31) correct
23%
(01:28)
wrong
based on 139
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In the figure above, arc QRO is a semicircle. What is the area of the circle with center O?
(1) The area of triangle PQO is 30.
(2) The length of QRO is 2.5π.
Attachment:
2016-01-04_0044.png [ 12 KiB | Viewed 3532 times ]
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BrainLab
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Joined: 10 Mar 2013
Last visit: 26 Jan 2025
Posts: 341
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Concentration: Finance, Entrepreneurship
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GMAT 1: 580 Q46 V24
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Bunuel
(1) Area of triangle = 30, clearly not sufficient, we cannot enforce it to be 5:12:13 trianlge
(2) If the length is equal to 2.5π then the diameter of the small circle is equal to 5 (whole length = 5π and circumference=π*d, hence d=5) Not sufficient
(1) + (2) Now we know that the small side of a triangle = 5 and from the Area formula PO*QO=60 -> PO=60/5=12, so we have a 5:12:13 triangle, hence PO=Radius=13. It's sufficient to calculate the area of the big circle.
Answer C
paidlukkha
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Schools: ISB '18 Great Lakes '18 SPJ PGPM"17 LBS '18 NTU '18 NUS '18
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BrainLab
where does it say QRO is 1/2 of the big circle
just says QRO is a semicircle
so E!
Bunuel
To calculate area of the circle with center O, we need to know the radius PO.
(1) => 1/2 *QO * PO = 30.
QO unknown => no way to know PO.
(2) => know QO. But how to know PO? No way
(1) + (2) => know QO => know PO => know area
C is correct
Bunuel
\(? = {S_{{\text{big}}\,\, \odot }}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,? = OP\,}\,\)
\(\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{\\
\,\left( 2 \right)\,\,\, \Rightarrow \,\,\,OQ = 5 \hfill \cr \\
\,\left( 1 \right)\,\,\, \Rightarrow \,\,\,30 = {{OP \cdot OQ} \over 2} \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\, = \,\,\,OP\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{C}} \right)\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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