Obra drove 160Ï€ meters along a circular track....

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Wed Jan 24, 2018 8:47 am

Obra drove 160Ï€ meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600Ï€ square meters, what percentage of the circular track did Obra drive?

A. 6.67%
B. 12.5%
C. 18.75%
D. 25%
E. 33.3%

The OA is the option E.

What is the equation I should set to get an answer here? Experts, I ask for your help. Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Wed Jan 24, 2018 8:47 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Thu Jan 25, 2018 8:28 am

Vincen wrote:Obra drove 160Ï€ meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600Ï€ square meters, what percentage of the circular track did Obra drive?

A. 6.67%
B. 12.5%
C. 18.75%
D. 25%
E. 33.3%

The OA is the option E.

What is the equation I should set to get an answer here? Experts, I ask for your help. Thanks in advanced.

We're given: r^2 * Ï€ = 57,600 * Ï€

r^2 = 57,600

r = 240. (Hopefully, you recognize that 24^2 = 576.)

If r = 240, then the circumference = 2Ï€r = 2*240*Ï€ = 480Ï€.

She's gone 160Ï€, or 160Ï€/480Ï€ = 1/3 = 33.33...%. The answer is E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Jul 28, 2019 9:04 am

Vincen wrote:Obra drove 160Ï€ meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600Ï€ square meters, what percentage of the circular track did Obra drive?

A. 6.67%
B. 12.5%
C. 18.75%
D. 25%
E. 33.3%

The OA is the option E.

What is the equation I should set to get an answer here? Experts, I ask for your help. Thanks in advanced.

Since the area enclosed by the circular track is 57,600Ï€ square meters, the radius of the track, r, can be determined by the equation:

Ï€r^2 = 57,600Ï€

r^2 = 57,600

r = âˆš57,600 = 240

Therefore, the circumference (or length) of the track is 2Ï€r = 2Ï€(240) = 480Ï€ meters. So Obra drove

160Ï€/480Ï€ = 1/3 or 33.3% of the circular track.

Answer: E

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