PS - Percentile

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Mon Jun 11, 2012 5:31 am

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

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Karthik
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Source: Beat The GMAT — Problem Solving | Mon Jun 11, 2012 5:31 am

gmat_and_me: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Sat Mar 05, 2011 9:14 amFollowed by: 5 members; Location: Bangalore; Thanked: 20 times; GMAT Score:770

by gmat_and_me » Mon Jun 11, 2012 6:30 am

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 ?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 11, 2012 8:32 am

karthikpandian19 wrote: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.

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Mon Jun 11, 2012 2:53 pm

OA is B

Regards,
Karthik
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