Gmat Prep Tough Geometry- Triangle

[khurram]

I think it has something to do with outer angle equal to inner to get the answer. But, now sure how to attack it.

Thanks
Khurram

[Stuart@KaplanGMAT]

Let's call angle PQR "x" and angle PRS "y". So, the question is:

what's y - x?

First thing to note: each statement gives the exact same info. So, the only possible answers to the question are (D) each one is sufficient and (E) not enough info.

This is tough without a diagram, so follow as best you can!

(1) QPR = 30

So, the other two angles in the top triangle sum to 150. We've already called angle PQR "x", so the other angle (QRP) is 150 - x.

Anqle QRP and y make a straight line, so QRP + y = 180. In other words:

(150 - x) + y = 180

Rearranging:

150 + y - x = 180

and subtracting 150 from both sides:

y - x = 30.

The question is "what's y - x", so (1) is sufficient.

Since statement (2) is identical to statement (1), it must also be sufficient: choose (D).

* * *

I'm sure there's some incredibly obscure rule that covers this particular question, but it's unlikely you'll need to know that rule on test day. However, the rules used in my explanation (angles of a triangle sum to 180 and angles in a straight line sum to 180) are essential GMAT knowledge.

[khurram]

Thanks

Stuart

You are the best.

Khurram

[amitansu]

As Stuart says : If we examine the two stems we can see both either ways say the same thing. So D could be the choice.

(Please refer the diagram which is in main question thread.It 's not attached here.)

From 1 : QPR is 30 degree.

So PQR+QRP=150
Now as per triangle rule, PRS=30+PQR (The extended/external angle of a triangle is sum of the two remote internal angles)
Now q asks PRS-PQR= ? => 30+PQR-PQR=30 SO sufficient

From 2 : PQR+PRQ=150 WHICH IS SAME AS QPR=30 so same solution as is given above.So sufficient.

[vinviper1]

Great explanations guys