Hi, there! I'm happy to help with this one.
What's tricky about this problem is that there are three different triangles in the diagram, and we have to apply the "180 degree Triangle Theorem" in each one.
First of all, from the diagram, we know in triangle PRS, that (angle SPR) + (angle PRS) + 90 = 180, or in other words, (angle SPR) + (angle PRS) = 90
In triangle PQS, we know that (angle SPQ) + (angle SQR) + 90 = 180, or in other words, (angle SPQ) + (angle PQR) = 90.
Set those two equal:
(angle SPR) + (angle PRS) = (angle SPQ) + (angle PQR)
(angle SPQ) - (angle SPR) = (angle PRS) - (angle PQR)
The question is asking: "the measure of angle PRS is how many degrees greater than the measure of angle PQR?" In other words, they are asking for (angle PRS) - (angle PQR), and our equation above tells us that: if we know (angle SPQ) - (angle SPR), then we know (angle PRS) - (angle PQR).
Statement #1: (angle QPR) = 30 degrees
We know that (angle SPQ) = (angle SPR) + (angle QPR) (big angle equals the sum of the two little angles the comprise it)
Therefore (angle SPQ) = (angle SPR) + 30 --> (angle SPQ) - (angle SPR) = 30 ---> (angle PRS) - (angle PQR) = 30
Statement #1 is sufficient by itself. .
Statement #2: (angle PQR) + (angle PRQ) = 150 degrees
Well, in triangle PQR, we know that: (angle PQR) + (angle PRQ) + (angle QPR) = 180 degrees
If (angle PQR) + (angle PRQ) = 150 degrees, then 150 + (angle QPR) = 180 degrees ---> (angle QPR) = 30, and we have the same information we had in statement #1, so statement #2 is also sufficient by itself.
Answer Choice D. Does that make sense?
Here's another GMAT DS question on the 180 degree Triangle Theorem, just for practice.
https://gmat.magoosh.com/questions/1009The question at that link should be followed by a video explanation of the answer.
Please let me know if you have any more questions.
Mike
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Mike McGarry
Magoosh Test Prep