Needing to find nearest percentage point

Question

In fall 2014, 32% of applicants with a Math SAT of 700 or more were admitted by a certain university, while 18% with a Math SAT of less than 700 were admitted. Further, 34% of all applicants had a Math SAT score of 700 or more. What percentage of admitted applicants had a Math SAT of 700 or more? (Round your answer to the nearest percentage point.)

Answer 1

Let's say 1000 people applied (this number isn't important as it cancels out later).

34% of these had a Math SAT >= 700, so 0.34 x 1000 = 340 people had a Math SAT >= 700

Obviously then, 1000 - 340 = 660 people had a Math SAT < 700.

32% applicants with a Math SAT >= 700 were admitted, so 0.32 x 340 people were admitted here.

18% with a Math SAT < 700 were admitted so 0.18 x 660 people here.

So required percentage = 100 * (number admitted with Math SAT >= 700) / (total admitted) =

100* (0.32 x 340) / (0.32 x 340 + 0.18 x 660) = 47.80316344, which is 48% to nearest percentage point.

Mike