Gmat Prep: circular cloth

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Hano: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Sat Nov 10, 2007 6:49 pm

by Hano » Mon Dec 03, 2007 8:59 pm

A circular cloth with a diameter of 20 inches is place on a circular tray of 24 inches. What fraction of the tray suface is not covered by the cloth?

A) 1/6
B) 1/5
C) 11/36
D) 15/36
E) 5/6

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Source: Beat The GMAT — Problem Solving | Mon Dec 03, 2007 8:59 pm

oct07: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Oct 09, 2007 6:48 pm

by oct07 » Mon Dec 03, 2007 9:08 pm

Rtray = 1/2(24) = 12
Rcloth = 1/2(20) = 10

We need to find:
(S tray - S cloth)/S tray
= (TT Rtray^2 - TT Rcloth^2) / TT Rtray^2 (divide TT for both sides)
= (Rtray^2 - Rcloth^2) / Rtray^2
= (12^2 - 10^2)/ 12^2
= 44/144
= 11/36

As is C

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