3Qs from gmat prep

For the 1st question,
we need to find angle PRS minus angle PQR
Statement 1 states that angle QPR = 30. Let angle RPS be x. Then angle PRS is 90-x. Angle PQR is 180 - (90+x+30) = 60-x
Thus angle PRS minus angle PQR is (90-x) - (60-x)=30

Statement 2 states that angles PQR + PRQ = 150. Let angle PQR=y. Then angle PRQ = 150-x. Also angle PRS = 180-(150-x)=30-x
Thus angle PRS minus angle PQR is (30-x) - (x)=30

Hence the answer is D ie both the statements satisfy.

What is the correct answer?

Statement 1 This gives us that there are 30 birds in the shop which is 1/5 of the pets. Thus the total no. of pets is 30*5=150. Thus, the no. of dogs is 150*1/3=50 dogs

Statement 2 - There are 20 more dogs. Let the total no.of pets be x. Thus x/3 - x/5 = 20. Solving, we get x=150. Thus, the no. of dogs is 150*1/3=50 dogs

The correct answer is D

Let the amount invested in X be x
Thus, the amount invested in Y (at 7% p.a) is 24000-x

Also let the rate of interest received on be y% p.a

Statement 1 The interest received from X and Y are identical. Thus, x*y/100 = (24000-x) *7/100
We cannot solve this equation any further because of 2 unknowns x and y.
Hence not sufficient

Statement 2 It only gives us the interest rate earned by X and no other data. Hence not sufficient

Combining both, from statement 2, we know that y=5%. Substituting the value of "y" in the above equation, we can solve for x.

Correct answer is C