Shaded Region

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anshulseth: Master | Next Rank: 500 Posts; Posts: 145; Joined: Mon Feb 16, 2009 8:41 am; Thanked: 2 times; Followed by:2 members

Shaded Region

by anshulseth » Wed May 06, 2009 12:37 am

6. In the figure above, two rectangles with the same dimensions overlap to form the shaded region. If each rectangle has perimeter 12 and the shaded region has perimeter 3, what is the total length of the heavy line segments?
(A) 15 (B) 18 (C) 21
(D) 22 (E) 23

Refer to the attached figure.

Please explain the working

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Source: Beat The GMAT — Problem Solving | Wed May 06, 2009 12:37 am

bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

by bluementor » Wed May 06, 2009 4:55 am

I'm assuming the heavy length segments are the outer shape of the diagram.

Have a look at the attached diagram.

let say the perimeter of the overlap (which is a triangle) = a + b + c = 3.

when both rectangles (rectangle 1 on the left, and rectangle 2 on the right) do not overlap, their respective perimeters are 12 and 12.

when they overlap, part of the perimeter of rectangle 1 is 'lost'. This lost section is c. the same way, part of perimeter of rectangle 2 is lost. This lost section of rectangle 2 is a+b.

So the perimeter of the diagram = (12 - c) + (12 - b - a)
= 24 - a - b - c
= 24 - (a + b + c)
= 24 - 3
= 21

Choose C.

-BM-

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