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GMAT-PREP Q 12

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mindadze
 Post subject: GMAT-PREP Q 12
 Post Posted: Sun Jan 22, 2012 2:18 pm 
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Students


Posts: 14
Hi,

Here is the screenshot of the problem: http://s16.postimage.org/a09a3adfp/Gmat_Prep.jpg

This was the 12th question I got and I went guessing, because I had no idea how to approach it and also because I was almost sure that I had no mistakes in previous questions.

Circumference of the circle is 18p. The minor arc PQ has a very small length, from answer choices the least was 2p. So i hit it. Guessed in Max 20-30 sec. The OA is A (2p).

Please explain how should this problem be SOLVED.

Thank you.
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mindadze
 Post subject: Re: GMAT-PREP Q 12
 Post Posted: Mon Jan 23, 2012 10:47 am 
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Students


Posts: 14
I think I arrived to the solution.

We coonect Q and O. Let X be the intersection of QO and PR.
Angle ORP= Angle QPX=35 degree
Angle PXQ= Angle OXR
Thus the triangles OXR and PXQ are similar.
Thus the lengths of Arc PO and of Arc QR are equal.
If we connect P with the center if the circle (C), then the Angle PCO should be the double of Angle PRO, hence Angle PCO=35x2=70 degree.

As mentioned the lengths of Arcs PO and QR are equal, and they both correspond to the angles (based on the diameter) with the measures of 70 degree. So in total 140 degree.

So 360 - 140 - 180=40 should equal to the length of the angle which corresponds to the Arc PQ.

Length of Arc PQ= 40/360*18p=2p.

Please have a look. Thanks.
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RonPurewal
 Post subject: Re: GMAT-PREP Q 12
 Post Posted: Wed Feb 01, 2012 2:37 am 
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ManhattanGMAT Staff


Posts: 7146
that solution works, but is unnecessarily elaborate. in particular, you definitely don't need to construct auxiliary lines.

* because the lines are parallel, we know that angles P and R have the same measure.
* so, both of them are 35°.
* inscribed angle is 1/2 the arc that it cuts off, so arcs OP and QR are 70° each.
* so, the arc you want is 40°.
* 40° is 1/9 of a whole circle, so find 1/9 of the circle's circumference.

your approach also works, but it may not be something you're able to formulate and execute within a GMAT timeframe.
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RonPurewal
 Post subject: Re: GMAT-PREP Q 12
 Post Posted: Wed Feb 01, 2012 2:38 am 
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ManhattanGMAT Staff


Posts: 7146
by the way, i'm extremely happy to see that you estimated the answer!
i wish more students would do that sort of thing (which, ironically, would be the very first thing that almost anyone would do upon encountering a similar situation in real life).
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