PS - Percentile

[karthikpandian19]

Melissa's best time in the 100 meter sprint was in the 70th percentile of the 70 runners at the City A Track Meet. Of the 110 runners at the City B Meet, held on the same day, only 15 ran times faster than Melissa's. If no other time was the same as Melissa's, then Melissa's time was in what percentile of the two cities' runners combined?


(A) 49th

(B) 80th

(C) 82.5th

(D) 85th

(E) 86th

[gmat_and_me]

Is the OA 80 ?

70 percentile => 30% of the people ran faster => 21 ran faster in A
15 ran faster in B => Town A and B together 36 ran faster => 36/180
=> 20% ran faster => in 80-th percentile ?

What is the OA ?

Cheers

[GMATGuruNY]

Melissa's best time in the 100 meter sprint was in the 70th percentile of the 70 runners at the City A Track Meet. Of the 110 runners at the City B Meet, held on the same day, only 15 ran times faster than Melissa's. If no other time was the same as Melissa's, then Melissa's time was in what percentile of the two cities' runners combined?


(A) 49th

(B) 80th

(C) 82.5th

(D) 85th

(E) 86th

Percentile means the percentage below.
In Melissa's race, the number of people who ran slower than Melissa = .7(70) = 49.
In the other race, since 15 times were faster than Melissa's, and no times were the same as Melissa's, the number who ran slower than Melissa = 110-15 = 95.
When the races are combined, the percentage with a slower time than Marissa's time = (49+95)/(70+110) * 100 = 80.

The correct answer is B.

[karthikpandian19]

OA is B