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GMAT prep - geometry

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GMAT prep - geometry [#permalink]

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New post 14 Apr 2009, 15:50
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A
B
C
D
E

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(N/A)

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0% (00:00) correct 100% (01:58) wrong based on 0 sessions

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Re: GMAT prep - geometry [#permalink]

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New post 14 Apr 2009, 16:06
First of all both statements give us the same info, so A & B are out in the case of guessing.

Now, the exterior angle of an angle in a triangle is equal to 180 - that angle. By giving us QPR they give us the difference between the exterior angles of the two triangles (the external angles of QPS and RPS). Since the two triangles share the right angle, that difference can only come from the angles PRS and PQR. The difference between them being 30 degrees.

I hope I made it clear enough, it's not easy to explain it.

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Re: GMAT prep - geometry [#permalink]

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New post 14 Apr 2009, 16:35
The Ans would be D - each statement alone is sufficient to answer the question

Question Stem : We need to find out angle PRS - angle PQR

Stmt 1 : angle QPR = 30

Let angle RPS be a
Sum of angles in a triangle = 180
So,
PSR + PRS + RPS = 180 ;
90+PRS+a = 180 ; PRS = 90 - a

using the same property of triangles for triangle QPS ;
PQS+QSP+QPS=180
PQS+90+30+a=180
PQS=60-a
or
PQR = 60 - a
Hence we know the difference between angle PRS & angle PQR
Sufficient

Stmt 2 : Angles PQR & PRQ = 150
which is nothing but angle QPR = 30 (from properties of triangles - sum of angles in a triangle = 180)
Sufficient

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Re: GMAT prep - geometry   [#permalink] 14 Apr 2009, 16:35
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