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The figure above represents a window, with the shaded regions represe

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Math Expert
Joined: 02 Sep 2009
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The figure above represents a window, with the shaded regions represe [#permalink]

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11 Aug 2016, 06:43
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The figure above represents a window, with the shaded regions representing openings for glass and the pale regions representing the wood panels between and around the glass. If the window is 4.5 feet high by 2.5 feet wide, and if each of the wooden panels is exactly 4 inches thick, what is the total surface area, in square inches, of glass in the window?(1 foot = 12 inches; figure not drawn to scale)

A. 189
B. 378
C. 448
D. 756
E. 1,620

[Reveal] Spoiler:
Attachment:

2016-08-11_1740.png [ 1.04 KiB | Viewed 1545 times ]
[Reveal] Spoiler: OA

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Re: The figure above represents a window, with the shaded regions represe [#permalink]

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11 Aug 2016, 08:11
1
KUDOS
size of window is 4.5*12=54 inch high and 2.5*12=30 inch wide.

2 glasses combined width = 30 - (three 4 inch wood plancks) = 30-12 = 18
1 glass's width=9

2 glasses combined height = 54 - (three 4 inch wood plancks) = 54-12 = 42
1 glass's height = 21

Area of 1 glass = 21*9 = 189 inch^2

Area of 4 glass = 4*189 = 756 inch^2

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Re: The figure above represents a window, with the shaded regions represe [#permalink]

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03 Sep 2017, 13:01
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Re: The figure above represents a window, with the shaded regions represe [#permalink]

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03 Sep 2017, 21:36
Bunnel help me to solve this problem

Kudos [?]: 4 [0], given: 91

Math Expert
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128641 [0], given: 12181

Re: The figure above represents a window, with the shaded regions represe [#permalink]

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03 Sep 2017, 23:20
SandhyAvinash wrote:
Bunnel help me to solve this problem

Please point out what is unclear in the solution here: https://gmatclub.com/forum/the-figure-a ... l#p1721423 Thank you.
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The figure above represents a window, with the shaded regions represe [#permalink]

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03 Sep 2017, 23:45
2
KUDOS
Given: height of window = 4.5 feet = 4.5*12= 54 inches
width of window = 2.5 feet = 2.5 *12 = 30 inches

Now given each wooden plank is 4 inches wide.

If you observe the figure width wise.. its => wood-glass-wood-glass-wood
=> 4inch+glass width+4inch+glass width+4inch= width of window = 30 inch
2* glass width = 30-12=18
=> glass width = 9inch

Same way if we observe window height wise.
wood 4inch
glass height
wood 4inch
glass height
wood 4inch
=Total height of window = 54 inch

=> 2*glass height = 54-12=42
glass height = 21

Now glass dimension = 21*9
Area of 4 glass windows = 4*9*21 = 756

+1 kudos if you like the solution.
Attachments

Window with glass.jpg [ 1.17 MiB | Viewed 257 times ]

Last edited by Nikkb on 04 Sep 2017, 22:41, edited 2 times in total.

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Re: The figure above represents a window, with the shaded regions represe [#permalink]

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04 Sep 2017, 18:48
why are you multiplying 2 with glass width. please provide clear solution for this thanks.

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Re: The figure above represents a window, with the shaded regions represe [#permalink]

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04 Sep 2017, 22:38
1
KUDOS
SandhyAvinash wrote:
why are you multiplying 2 with glass width. please provide clear solution for this thanks.

"
If you observe the figure width wise.. its => wood-glass-wood-glass-wood
=> 4inch+glass width+4inch+glass width+4inch= width of window = 30 inch
2* glass width = 30-12=18
=> glass width = 9inch
"

If you observe the figure: ( check attached hand drawn figure as well, i have mentioned measurements in it)

so if we go horizontally ie width wise.. you will see there is a wooden slab than a glass window than again wooden slab than again a glass window than at end again a wooden slab.
So in width we see 3 wooden slab and 2 glass windows.
So basically total width of window = 3* wooden slab width + 2* glass width.

That's why in calculation we have multiplied width by 2.

Also same will be case if go with height wise. As if you check vertical length, than also we will see 3 wooden slab and 2 glass contributing to total height of window.

Kudos [?]: 59 [1], given: 59

Re: The figure above represents a window, with the shaded regions represe   [#permalink] 04 Sep 2017, 22:38
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