According to me the answer should be "D"

Basically we need to find PRS-PQR

1) Statement 1

PRS is an external angle of triangle PQR
So QPR+PQR = PRS
Its given that QPR is 30 degree
So PRS-PQR=30

Statement 1 alone is sufficient

2) Statement 2

PQR+PRQ=150
So QPR=30 degree...which is the 1st statement.
If we proceed in the same manner as above we can see even statement 2 alone is sufficient.

The answer is "D"

First of all, the two statements are identical (if one angle is 30 degrees, then the other two will obviously add up to 150). So there are only two choices: either D or E.

Now, statement 1 tells us, basically, that whatever the angle RPS is of the smaller triangle (points PRS), the QPS angle of the larger triangle (points PQS) is that plus 30 degrees. That means that PQR must be less than PRS also by 30 degrees (since both are right triangles and their unknown angles add up to 90 degrees). So, it's sufficient.

Since statement 2 is identical to statement 1, it is also sufficient.

Deepthi Subbu wrote:Can someone help me with this problem?

Hi Deepthi, Please confirm D is correct.Thanks!