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GMATPrep Geometry

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MBAlad
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GMATPrep Geometry [#permalink] New post   07 Dec 2006, 16:45
Tricky one



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Re: GMATPrep Geometry [#permalink] New post   07 Dec 2006, 17:47
Ans: C

Angle QRS = r
Angle RTP = t
T+r = 90 degrees
Z (Angle RQS) +x+y (Angle TUS) = 180


1) Angle RSQ = Angle RQS = z INSUFF
r = 180 -2z

2) Angle SUT = Angle UST = y INSUFF
T = 180 -2y

Combining and solving we get 3 equations of 3 variables x, y,z. Thus can be solved


X+y = r+z
Z+x+ (180-2y) = 180 =>x+z = 2y
X+y-z = (90-t) = (90-180+2y)
And x+y+z = 180
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Re: GMATPrep Geometry [#permalink] New post   07 Dec 2006, 18:03
from 1. <RQS = <RSQ
from 2. <TUS= <TSU

from diagram
<RSQ+x+<TSU=180
=> <RSQ+<TSU = 180-x

aslo from PQSU
X+<SQP+<P+<PUS =360
=>x+180-<RQS+90 + 180-<TUS=360
=>x+90-(<RQS + <TUS) =0
=>x+90 -(<RSQ+<TSU)=0
=>x+90 -(180-x)=0;
=>x= 45

so c is the ans.
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Re: GMATPrep Geometry [#permalink] New post   11 Dec 2006, 02:50
Quote:
Ans: C

Angle QRS = r
Angle RTP = t
T+r = 90 degrees
Z (Angle RQS) +x+y (Angle TUS) = 180


1) Angle RSQ = Angle RQS = z INSUFF
r = 180 -2z

2) Angle SUT = Angle UST = y INSUFF
T = 180 -2y

Combining and solving we get 3 equations of 3 variables x, y,z. Thus can be solved


X+y = r+z
Z+x+ (180-2y) = 180 =>x+z = 2y
X+y-z = (90-t) = (90-180+2y)
And x+y+z = 180


confused about the part in orange. hsampath, can you explain please?
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Re: GMATPrep Geometry [#permalink] New post   11 Dec 2006, 13:25
the answer is C
Each st individually is insuff.

st 1 says qr =rs thus ang qrs= ang qsr =y and ang rqs =180-2y and pq s=2y
st2 says st=tu thus ang ust = ang stu =z and ang sut =180-2z and ang sup= 2z
Also y+z=90 (from the rt triangle)

Now
x+2y+2z+90=360
x=270-2(y+z)
x=270-180=90
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Re: GMATPrep Geometry [#permalink] New post   26 Dec 2006, 23:56
hsampath wrote:
Ans: C

Angle QRS = r
Angle RTP = t
T+r = 90 degrees
Z (Angle RQS) +x+y (Angle TUS) = 180


1) Angle RSQ = Angle RQS = z INSUFF
r = 180 -2z

2) Angle SUT = Angle UST = y INSUFF
T = 180 -2y

Combining and solving we get 3 equations of 3 variables x, y,z. Thus can be solved


X+y = r+z
Z+x+ (180-2y) = 180 =>x+z = 2y
X+y-z = (90-t) = (90-180+2y)
And x+y+z = 180


I don't get the red part... can someone explain please? :? why these angles make 180?
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Re: GMATPrep Geometry [#permalink] New post   27 Dec 2006, 02:51
u2lover wrote:
hsampath wrote:
Ans: C

Angle QRS = r
Angle RTP = t
T+r = 90 degrees
Z (Angle RQS) +x+y (Angle TUS) = 180


1) Angle RSQ = Angle RQS = z INSUFF
r = 180 -2z

2) Angle SUT = Angle UST = y INSUFF
T = 180 -2y

Combining and solving we get 3 equations of 3 variables x, y,z. Thus can be solved


X+y = r+z
Z+x+ (180-2y) = 180 =>x+z = 2y
X+y-z = (90-t) = (90-180+2y)
And x+y+z = 180


I don't get the red part... can someone explain please? :? why these angles make 180?


From S1 and S2:
angles RQS=RSQ;TUS=TSU
Since angleRSQ+x+angleTSU=180(straight line),angleRQS+x+angleTUS=180
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Re: GMATPrep Geometry [#permalink] New post   27 Dec 2006, 07:02
1. Statements 1 or 2 are not sufficent hence A,B and D are ruled out.
2.From Statement 1,
i) Triangle QRS is isoscles, assume, angles RQS,RSQ be A degrees
ii)Let Angle QRS be C
iii)2A+C = 180------------------------I
3) From Statement 2,
i) Triangle STU is isoscles, assume, angles TSU,TUS be B degrees
ii)Let Angle STU be D
iii)2B+D = 180------------------------II
4) From the traingle PRT,
i)C+D =90----------------------------III
ii)A+X+B=180------------------------IV
5)Solving I,II and III,
2A+2B +C+D = 360
A+B = 135 -------------------------------V
6) From IV and V,
x = 45!

Guess it is clear!
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Re: GMATPrep Geometry [#permalink] New post   27 Dec 2006, 09:42
thanks guys!!! things are clear today :-D the best part is that you don't have to solve it... just understand how to do it.
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Re: GMATPrep Geometry [#permalink] New post   29 Dec 2006, 14:07
MBAlad wrote:
Tricky one


-----------------------
C


1) , 2) aren't suffi..

Together:
PSQ + x+UST = 180 ---a)
90+x+(180-UST) + (180-PSQ)=360 --b)

frm a) & b)

90+x +x =180 -> x=45

C) is the answer
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Re: GMATPrep Geometry [#permalink] New post   31 Dec 2006, 10:07
It´s C.

By simple inspection of the figure, you notice that neither (1) nor (2) can be suff for arriving at a single value for x. Thus, right away you use (1) and (2) together and, by working on the inner angles formed by the 3 adjacent shapes, you get x = 45.
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Re: GMATPrep Geometry [#permalink] New post   23 Jan 2007, 05:54
sorry!!! to post this in this section of the forum......

But can anybody help me how I can post a new question in the respective section. I tried to post on geometry problem in the section,, but it says only moderator can initiate a question...please help soon..

Thanks!!



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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Re: GMATPrep Geometry [#permalink]
23 Jan 2007, 05:54
Moderator:
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