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what is x

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Director
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Joined: 10 Feb 2006
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what is x [#permalink] New post 25 Nov 2007, 18:39
Please provide details. Thanks
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CEO
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Joined: 17 Nov 2007
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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 [#permalink] New post 25 Nov 2007, 22:38
Expert's post
C

1. or 2. it is obviously that 1 and 2 along are insufficient. For 1 statement we can move U along PT to change angle x

1&2. QRS and UTS are isosceles triangles

angle(QSR)= (180-angle(QRS))/2
angle(UST)= (180-angle(UTS))/2

x+angle(QSR)+angle(UST)=180 ==>
x=180- (180-angle(QRS))/2-(180-angle(UTS))/2=(angle(QRS)+angle(UTS))/2

but for right triangle: angle(QRS)+angle(UTS)=90

Therefore, x=90/2=45 sufficient
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Re: what is x [#permalink] New post 25 Nov 2007, 23:23
alimad wrote:
Please provide details. Thanks


Wow thanks for posting this. After working on this for about 6minutes, i finally solved this problem. I had this on a previous GPrep and guessed C. I wasnt actually able to solve for X though this time around.

Please see drawing.

Ok we have angle X.

S1: for the smaller triangle we have z and y and y. z+2y=180* from here we cannot figure anything else out. Insuff.

S2: we have angle n, and 2 w's. Same as s1, though cannot figure anything else out.

Together we have x+y+w=180*

we also have 2y+z=180*
n+2w=180*.


No look at big triangle we have angles z, 90*, and n. so z+n+90*=180*

z+n=90*.

heres the trick to solve this: add

2y+z=180*
2w+n=180*

we have 2y+2w+z+n=360*---> plug in for z+n--> 2y+2w+90*=360*

y+w=135* No plug into x+y+w --> x= 45*


Answer is C.
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Re: what is x   [#permalink] 25 Nov 2007, 23:23
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