GMAT Prep - Triangles

[TGE]

Hello again,

Having problems trying to figure out the following problem (may need to zoom in on the image):




OA is D.

I know both effectively give the same information, but don't know how to use it solve the problem. Thanks for your help.

[dumb.doofus]

SPR + PRS = 90 --- (1)

SPR + 30 + PQS = 90 ---- (2)

(2) - (1)

=> 30 = PRS - PQS (PQS = PQR, so same thing)

hence D

[myohmy]

If you know the measure of angle QPR is 30 (which you know from either of the two statements), then you know that:

LPQR + LPRQ = 150

and
LPRQ = 150 - LPQR
LPQR = 150 - LPRQ

PRQ and PRS must add up to 180:
LPRS = 180 - (150 - LPQR)
LPRS = 30 + LPQR

So the answer is D.

[TGE]

Thanks, guys. Two great ways of getting to the answer.

[iamcste]

Hello again,

Having problems trying to figure out the following problem (may need to zoom in on the image):




OA is D.

I know both effectively give the same information, but don't know how to use it solve the problem. Thanks for your help.

Yes both statments the samE

Statement 2 , PRQ=150- PQR....3.
PRQ=90+RPS..Exterior---1
PRS+RPS=90..SUM of angles of a trainagle
therefore RPS=90-PRS....2

SUB 2 IN 1

PRQ=90+90-PRS=180-PRS....4

EQUATING 3 and 4

150-PQR=180-PRS

Solve for PRS-PQR

As both statements express the same, D