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Data Sufficiency (Triangles)

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Tsadori Newbie | Next Rank: 10 Posts Default Avatar
Joined
16 Nov 2006
Posted:
4 messages

Data Sufficiency (Triangles)

Post Sun Jan 21, 2007 1:39 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    SOURCE: GMATPrep

    Help please! (See attached image)
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    Argen Junior | Next Rank: 30 Posts Default Avatar
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    Post Thu Mar 01, 2007 2:45 pm
    It's intuitive that either alone is not sufficient, so lets think about both statements together. Lets label some angles here: Let angles QRS=y, RQS=QSR=a, STU=z, UST=TUS=b. Now, y+z=90 because triangle RPT is a right triangle. We observe that y=180-2a and z=180-2b. So 180-2a+180-2b=90, which simplifies to 270-2(a+b)=0. We also observe that a+b+x=180, so a+b=180-x. Then 270-2(180-x)=0, and x=45. So the answer is C.

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