Hello,

I am having trouble with the following problem. I don't understand how angle QPR is sufficient to answer the question. Please enlighten me :shock:

PRS = QPR + PQR (exterior angle of a triangle is equal to sum of two interior angles)
PRS - PQR = QPR = 30. (1) is sufficient.
(2) provides the same information as (1).

Hence, (D).

-givemeanid

I forgot about that rule! It makes sense now :)

givemeanid has got it! You do need to make sure you know that exterior angle rule to get a high score on the test. :)

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

Does this rule only apply to right triangles?

Nope, external angle rule applies to any triangles.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

eh, the exterior angle rule is nice, but you don't need it to address this question.
in fact, you don't ever need the exterior angle rule; anything you can do with that rule, you can also do in a more roundabout fashion by just using the combination of two very basic facts: (1) 180° in a triangle, (2) 180° in a straight line.
granted, that approach will take longer than the exterior angle approach, but the exterior angle approach is only shorter if you think to use it right away. if you don't recognize the opportunity to use the exterior angle theorem RIGHT AWAY, then don't bother with it; just use 180° in a straight line and 180° in a triangle instead. just be prepared to deal with some pretty nasty algebra in some cases.

in this problem:
let angle QPR = 30°
let angle RPS = x°

then
using triangle PRS, we have x + 90 + angle PRS = 180°
so, angle PRS = (90 - x)°

using triangle PQS, we have (x + 30) + 90 + angle PQS = 180°
so, angle PQS = (60 - x)°

now (90 - x) is greater than (60 - x) by a margin of exactly thirty, so this is sufficient to answer the problem.

notice that the exterior angle theorem isn't necessary to do this, although it certainly makes for a shorter and more elegant solution. don't sweat it too hard, though; unless you're really weak in algebra, it's not an essential piece of knowledge.
remember that there are no style points.

Sorry, maybe I'm missing something, just came across this same problem. I understand the exterior angle rule as stated, but in this case, we're only being given one of the angles that we need to add up to find PRS, aren't we? If I understand the exterior angle rule, correctly, then PRS=PQR+QPR.

In the problem, we're given the measure for only one of them (QPR) in 1, so how is that alone sufficient to find the answer?

Similarly, in 2, we're given the sum of two angles that allow us again to determin that QPR=30 degrees, but I don't see how we're able to find out what PQR is? Help?

did you read the post directly above yours?

the answers to these questions are contained in the post directly above yours (the one written by me, dated 13 Oct 2008 05:34 am).

as an aside, you will never actually NEED the exterior angle theorem to solve a problem; it's just a shortcut that will save you approximately 10-15 seconds when it can be employed.

Thank you Ron, your explanations are fantastic!

glad it helps.

Not gonna lie, this one is really frustrating me. I full understand how to solve this using Ron's method, but how are some of you solving this using the exterior angle method?

Can I please get a step-by-step breakdown of how to solve this using the exterior angle method, talk me down like I'm 5 :).

in lieu of answering this question, i'm just going to repeat what i typed above:


perhaps the other posters will step up and explain the whole exterior angle thing, but i think it's much more important to emphasize the fact that you will never, ever NEED the exterior angle theorem. you will always be able to arrive at the same result(s) by just using repeated subtraction from 180 degrees.

This is probably too late for the original poster, but it took me a while to figure out why the external angle works here.

Since PRS = QPR + PQR, then PRS = 30 + PQR.
Therefore, PRS is 30 degrees greater than PQR.

I kept looking for a number for PQR to subract from when I only needed to know the difference.

the single most valuable thing you can learn about data sufficiency: if you seek the wrong information, you WILL get the wrong answer in almost all cases.
the problems are specifically written so that you have to focus on the correct information -- and ignore information that you don't actually need -- in order to solve them.