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njvenkatesh
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GMATprep Math help 13 Jun 2006, 11:11
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Please help with this Geometry DS

Thanks in advance



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tl372
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GMATprep Math help Updated on: 13 Jun 2006, 12:39
Originally posted by tl372 on 13 Jun 2006, 12:38.
Last edited by tl372 on 13 Jun 2006, 12:39, edited 1 time in total.
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oops..
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tl372
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GMATprep Math help 13 Jun 2006, 12:38
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This was a hard one. I guessed E at first and then had to go back to re-evaluate. Definitely spent too much time on this problem...if I had gotten this on the exam, probably would have guessed C or E and moved on.

See attached jpeg for a diagram. I assigned three more variables to the picture based on the information.

Came up with the following formulas and then tried to re-arrange them to see if I could come up with the value of x. With only 3 formulas and 4 variables, I can't deduce that I can find the value of x. Took a look closer:

90+(180-2p)+z = 180 (using triangle PRT)
2y+z = 180
p+x+y = 180


First - find z
90+180-2p +z = 180
180-2p+z = 90
z= 2p-90

The plug this into the equation 2y+z = 180
2y + (2p - 90) = 180
y+p = 135

Last, plug into last equation:
p+x+y = 180
x+135 = 180
x = 45

2 statements together - Sufficient

Any other thoughts on easier ways to solve?
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njvenkatesh
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GMATprep Math help 13 Jun 2006, 12:44
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Excellent Thanks ...
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kapslock
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GMATprep Math help 13 Jun 2006, 12:57
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njvenkatesh
Please help with this Geometry DS

Thanks in advance
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Some conventions for solving this problem,

Assume < QRS = z

From 1. QR = RS. Therefore,
< RQS = < RSQ.
x cant be computed because x + < RSQ + < USQ = 180 and we don't know either of them. Thus, insufficient.

From 2, exactly the same situation as 1. Insufficient.

Combining 1 and 2, look at the diagram.
< QRS = z.
Therefore, < UTS = 90-z.
Also, <SUT + <UST + <UTS = 180,
or, <SUT+<UST + 90-z = 180
=> SUT+UST = 90+z
Since SUT = UST, both are (90+z)/2

On the other side,
SQR + QSR + z = 180
=> SQR = QSR = (180-z)/2

Since RSQ + x + UST = 180,
(180-z)/2 + x + (90+z)/2 .............................. (A)

Consider the quadrilateral QSUP,
<SUP + 90 + SQP + x = 360
Since SUP = 180 - SUT, and SQP = 180 - SQR, we get
180 - (90+z)/2 + 90 + 180 - (180-z)/2 + x = 360 ................(B)

Thus we have 2 equations and 2 variables, and thus solvable.

Hence C.

Hope that helps.
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GMATprep Math help 13 Jun 2006, 13:00
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Sorry forgot the attachment ...
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jaynayak
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GMATprep Math help 13 Jun 2006, 23:48
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Will go with C,

1) Let <RQS be m, hence <RSQ = m
Not suff

2) Let <SUT be n, hence <UST = n
Not suff

Together.

R+P+T =180
R+T = 90

R = 180-2m and T = 180-2n
hence
180-2m + 180-2n = 90
m+n = 270/2

Also m+n+x =180
Hence We can find X



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