IMO D

say angles RPS: a, PRS: b, PQS: c

Stment: 1
in triangle PRS: a+b=90 (sum of all is 180 and rt angled at S)...1
in triangle QPS: a+30+c=90 (sum of all is 180 and rt angled at S)
or a+c=60.....2

subtracting 2 from 1 we get b-c=30 , hence statement 1 sufficient

Statement: 2: PQR+PRQ=150, it follows that QPR=30, which is what we started statement 1 with, hence sufficent

scoobydooby wrote:
Statement: 2: PQR+PRQ=150, it follows that QPR=30, which is what we started statement 1 with, hence sufficent

Can you explain the concept behind how you found Statement 2 sufficient?

Thanks

ReenaMo wrote:

scoobydooby wrote:
Statement: 2: PQR+PRQ=150, it follows that QPR=30, which is what we started statement 1 with, hence sufficent

Can you explain the concept behind how you found Statement 2 sufficient?

Thanks

In triangle QPR, PQR+PRQ=150, or QPR=30 (sum of all angles is 180, two are 150, and the third is therefore 30). we started with this info, ie QPR=30 in statement 1 and found it to be sufficent, here also we are down to the same information. it is therefore sufficient.

Got it - that was my mistake. I read one of the angles incorrectly. Thanks!