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# In the square above, 12w = 3x = 4y. What fractional part of the square

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Director
Joined: 27 May 2008
Posts: 520
In the square above, 12w = 3x = 4y. What fractional part of the square  [#permalink]

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04 Aug 2008, 10:34
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In the square above, 12w = 3x = 4y. What fractional part of the square is shaded?

A) 2/3

B) 14/25

C) 5/9

D) 11/25

E) 3/7
Manager
Joined: 14 Jan 2006
Posts: 85
Schools: HKUST
Re: In the square above, 12w = 3x = 4y. What fractional part of the square  [#permalink]

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04 Aug 2008, 10:42
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durgesh79 wrote:
Attachment:
square.PNG

In the square above, 12w = 3x = 4y. What fractional part of the square is shaded?

A) 2/3

B) 14/25

C) 5/9

D) 11/25

E) 3/7

let w = 1, x = 4, y = 3
area of square = (w+x)^2 = (5)^2 = 25
area of unshaded region : (1/2*1*4) + (1/2*1*4)+(1/2*1*2)+1/2*4*3)
=2+2+1+6 = 11
area of shaded region/area of square = (25-11)/25 = 14/25

Therefore, B
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Posts: 1632
Location: New York
Re: In the square above, 12w = 3x = 4y. What fractional part of the square  [#permalink]

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04 Aug 2008, 10:49
durgesh79 wrote:
Attachment:
square.PNG

In the square above, 12w = 3x = 4y. What fractional part of the square is shaded?

A) 2/3

B) 14/25

C) 5/9

D) 11/25

E) 3/7

= 1/2 *w*x + 1/2*w*x +1/2 * w * 2w* + 1/2 * x * Y
= w* 4w + w*w + 1/2 * 4w * 3w
= 11 w*w

Total square area = (w+x)*(w+x) = 25 w*w

area shaed fraction = 1- (11/25) = 14/25

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Director
Joined: 27 May 2008
Posts: 520
Re: In the square above, 12w = 3x = 4y. What fractional part of the square  [#permalink]

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04 Aug 2008, 10:59
correct OA is B
thanks guys
Senior Manager
Joined: 06 Apr 2008
Posts: 367
Re: In the square above, 12w = 3x = 4y. What fractional part of the square  [#permalink]

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05 Aug 2008, 02:10
durgesh79 wrote:
Attachment:
square.PNG

In the square above, 12w = 3x = 4y. What fractional part of the square is shaded?

A) 2/3

B) 14/25

C) 5/9

D) 11/25

E) 3/7

IMO B)

Let w =1, x=4, y=3

Area of square = 25

Are of non-shaded area = Area of four triangles = 11

Area of non-shaded area = 14/25
Intern
Joined: 21 Jan 2010
Posts: 3
Re: In the square above, 12w = 3x = 4y. What fractional part of the square  [#permalink]

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21 Jan 2010, 19:41
key fact to keep in mind to solve this question:

total area of the square - areas of 4 triangles / total area of square
Manager
Joined: 27 Jul 2010
Posts: 149
Location: Prague
Schools: University of Economics Prague
Re: In the square above, 12w = 3x = 4y. What fractional part of the square  [#permalink]

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02 Feb 2011, 07:10
faust1 wrote:
key fact to keep in mind to solve this question:

total area of the square - areas of 4 triangles / total area of square

Yes, it is important not to forget that, otherway you loose everything ang pick D
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Re: In the square above, 12w = 3x = 4y. What fractional part of the square  [#permalink]

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02 Sep 2017, 01:27
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Re: In the square above, 12w = 3x = 4y. What fractional part of the square   [#permalink] 02 Sep 2017, 01:27
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