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We dont know anything about RQ
1. RQ can be anything between >1 and <2x+3 The largest angle is always oppostite to the largest side ... insufficient as we cant say for sure which side is largest
Together ... insufficient same reason as above!
from mba.com Gmat Free Prep Test Software GMAT Practice Test 1
Figure: A right triangle with points S (the right angle), P and Q. from point P, another line extends ending between Q and S. The endpoint of this line is point R.
Basically, the figure has two right triangles - Triangle PSQ and Triangle PRS with Triangle PRS inside Triangle PSQ.
In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?
(1) The measure of angle QPR is 30 degrees. (2) The measure of angles PQR and PRQ combined are 150 degrees.
Hopefully I drew the triangle right... anyway,
(1) From this we know the angle of SPQ (60), but we don't know where point R falls along line SQ, so (1) isn't enough. (2) From this we know RPQ is 30, I don't think we can be sure of anything else... (Combined) We can find QPR & we can find out PRS, this is enough.
I would probably go with answer (C), but I still have a nagging feeling that we could find out from (2) alone, so I'm not entirely sure.
Okay... now I've figured it out (well, my mom figured it out)... the CORRECT answer is (B), you can indeed find out the answer from (2)alone.
We can solve this algebraically: Let PQR=A; Let PRQ=B; Let PRS=C;
We'll subtract the first equation from the second equation, this would eliminate B on the left side of the equal sign, and leave us with 30 degrees on the right side. This leaves us with: A-C = 30 degrees. We don't know the precise values of A & C, but we don't need to know, we've algebraically proven that the difference is 30 degrees (correction, my mom has proven that the difference is 30).
great solution, but doesnt statement 1 and 2 give us the same information, wouldnt the answer be D?
I fail to see how (1) provides the same information as (2). Could anyone explain?
From what someone said ("(1) From this we know the angle of SPQ (60), but we don't know where point R falls along line SQ, so (1) isn't enough."), I don't see that one either. How should we know anything about SPQ just by statement 1?