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[sharbhund]

I originally took the GMAT back in college and did pretty well on it (720), but that score has expired now. I downloaded the official GMATPrep software to see how my score would compare to it now without doing any studying (I've gotten 10% dumber over the years, which seems about right).

I haven't taken a geometry class in 12-15 years, however I was fairly confident that I got this question correct:

I thought the answer was E, but apparently it's D. Can someone explain this to me? I don't know how you can figure out the measure of these angles unless you assume that PS = RS. Am I missing something, or is the GMATPrep answer wrong?

 

[Dartastic]

I read the question wrong. Each answer gives you enough information to determine what each angle in each triangle is. When you can do that, you can determine the difference between the angles. I hate the math section; when I took the GMAT last year I DESTROYED both English sections, yet bombed the match section. Anyway, good luck.

 

[Bananakin]

Well, angle PRS = 180 - PRQ, since the angles are complementary. Then PRQ = 180 - QPR - PQR, since those angles form a triangle. So PRS = 180 - (180 - QPR - PQR) = QPR + PQR. With either of those two statements we know that QPR is 30 degrees, so PRS = PQR + 30, and we're done (since we only need to know the difference between PRS and PQR).

 

[surazal]

First, you should realize that statement 1 and 2 give you the same information. If angle QPR is 30, then the other two angles in the triangle QPR will add up to 150. Which is statement 2.

As for why there is enough information, you know two things.

1) PQR + PRQ = 150
2) PRS + PRQ = 180

Subtract the equations and you get
PRS - PQR = 30

edit:beaten

 

[sharbhund]

I don't think both hints do give you enough information to figure out all the angles. If you know that QPR = 30, then you can assume that PQR + PRQ =150, they both tell you the same thing.

Ironically, the one question I remember getting wrong when I originally took the GMAT was another geometry question, because I couldn't remember what an isosceles triangle was.

 

[sharbhund]

Thanks, that makes sense now. I was just thinking about this question the wrong way. I was trying to figure out the degrees of each angle.

I've been debating whether to spend the $1600 for the courses, because I've forgotten how to do a lot of this stuff.

 

[Evlar]

Discovery of the difference between PRS and PQR from Statement 1:
PSQ = 90deg
QPR = 30deg
PQS = PQR
QPS = RPS + QPR
QPS = RPS + 30deg

PQS = 180deg - (PSQ + QPS)
PQS = 180deg - (90deg + RPS + 30deg)
PQS = 60deg - RPS = PQR
RPS = 60deg - PQR

PRS = 180deg - (PSQ + RPS)
PRS = 180deg - (90deg +60deg - PQR)
PRS = 30deg + PQR

Demonstration that Statement 2 is equivalent to Statement 1:
PQR + PRQ = 150deg
QPR = 180deg - (PQR + PRQ)
QPR = 180deg - (150deg)
QPR = 30deg

THEREFORE Statement 1 and Statement 2 are equivalent. Since Statement 1 alone can be used to derive the difference between PRS and PQR, its equivalent Statement 2 alone can be used to derive the difference as well. D.