GMAT prep test question in geometry - it's driving me crazy!?

Question

Construct a triangle PQS such that angle PSQ is a right angle.  Now construct a line segment PR such that R lies between Q and S.

How many degrees is angle PRS greater than PQR?

a)  QPR = 30°
b)  PQR + PRQ = 150°

A)  I can find the answer with just eqn(a)
B)  I can find the answer with just eqn(b)
C)  I can find the answer with eqn(a) AND eqn(b)
D)  Both of these equations together do not give enough info to get an answer.

Saying that QPR = 30° and that the sum of the other two angles is 150° is really the same piece of information, right?  I know that PRQ + and PRS are complementary (=180°) but since QP and PR are not parallel, we know nothing about their angular measures.  Or I am missing some piece of critical info?

T · Accepted Answer

You are correct that a) and b) are saying the same thing.  However you can come up with answer.  Using b)

PQR + PRQ = 150
PRS + PRQ = 180

Subtract 1 from 2

PRS - PQR = 30

Therefore PRS is 30 degrees greater than PQR.

That is just one way to go about it.  You could also just use a) to solve.

I would argue that either A), B) or C) would be right answers.

? · Answer

You got it - "is really the same"
 D  not enough info.   There are an infinite number of triangles that can be done with the 30 degrees being held and the relation of the two base angles varies constantly.  Do a quick drawing.

Anonymous · Answer

The answer is (A)

PRS = PQR + QPR  ...(External angle equals sum of internal opposite angles, from triangle PQR)

I.e. PRS = PQR + 30

potlyfe · Answer

You are exactly right. they give you the exact same piece of information in two different ways. 

however these other guys are right the angle difference is 30 degrees. based on the opposite angle rule.

Trending News

GMAT prep test question in geometry - it's driving me crazy!?

4 Answers