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DS_14 - Geometry problem

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by desihokie » Thu Jan 17, 2008 11:38 pm
found this on powerprep.
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Source: — Data Sufficiency |
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by camitava » Fri Jan 18, 2008 2:27 am
IMO E. What's the OA?
--- Sorry my miss! I really overlooked that the triangle is a right-angled triangle. Sorry once again! Now I agree with Simplyjat. It shhould be D.
Last edited by camitava on Fri Jan 18, 2008 3:20 am, edited 2 times in total.
Correct me If I am wrong


Regards,

Amitava
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by simplyjat » Fri Jan 18, 2008 2:51 am
Answer is D, both statements are alone sufficient to solve the problem.

we know from the stem that
1. PSQ = PSR = 90
2. QPS = QPR + RPS
3. PQR = PQS


The first statement says that QPR is 30
We know that
PSR + SRP + RPS = 180 = PSQ + SQP + QPS
=> SRP + RPS = SQP + QPS [PSR = PSQ = 90]
=> SRP + RPS = SQP + RPS + 30 [ QPS = RPS + QPR = RPS + 30 ]
=> SRP = SQP + 30...
Thus PRS is 30 degrees more than PQR...

The second information says that PRQ + RQP = 150.
We know that
PRQ + RQP + QPR = 180.
=> QPR = 30 which is same as the information stated in first...
simplyjat
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by desihokie » Fri Jan 18, 2008 8:00 am
I was just looking at the problem again and i see that

PRS = QPR+PQR in all cases.
-> PRS - PQR = QPR

In other words, whenever QPR>0, PRS - PQR >0 OR PRS IS GREATER THAN PQR.
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