Quick high school maths refresher -
Sum of all angles of a triangle equals 180 degrees. -------- (A)
Supplementary angles on a line sum to 180 degrees. ------ (B)

Now in the question above, We need PRS - PQR,

Statement 1:
QPR = 30
From A above - QPR + PQR + PRQ = 180
This implies PQR + PRQ = 150
or, PRQ = 180 - PQR ---------(C)

Also PRQ and PRS are supplementary. So from B above, PRQ + PRS = 180
Substituting for PRQ from C, 180 - PQR + PRS = 150
or, PRS - PQR = 30.

Thus 1 is sufficient.

Statement 2:
PQR + PRQ = 150
or, PRQ = 180 - PQR ---------(D)

Also PRQ and PRS are supplementary. So from B above, PRQ + PRS = 180
Substituting for PRQ from C, 180 - PQR + PRS = 150
or, PRS - PQR = 30.

Thus 2 is sufficient.

Since both statements alone are sufficient, answer is D.

one approach u can always remember

whenever u r stuck... and dont know how to proceed with the problem...
try picking numbers...

statement 1:

in your figure take <RPS = 30
therefore <PRS = 180 - (90 + 30) = 60

since <RPS = 30 , <QPS = 30 + 30 = 60
therefore <PQR = 180 - (90 + 60) = 30

Now <PRS - <PQR = 30

as soon as u get this answer it should hit u that the answer will be the same no matter what number u start with...

u can further try with 20 or something...

statement 2 says essentially the same thing as statement 1...
so IMO: D

Hope it Helps...

HI! Neeraj,


Very good technique ,
Thanks man,