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

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Bunuel
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In the square above, 12w = 3x = 4y. What fractional part of the square [#permalink] New post   10 Nov 2014, 03:15
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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

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B
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PareshGmat
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Re: In the square above, 12w = 3x = 4y. What fractional part of the square [#permalink] New post   10 Nov 2014, 03:35
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12w = 3x = 4y

x = 4w &

y = 3w

Area of square \(= (5w)^2 = 25w^2\) .............. (1)

Area of un shaded region (4 right triangles) \(= \frac{1}{2} w * 4w + \frac{1}{2} 2 w^2 + \frac{1}{2} 4w * 3w + \frac{1}{2} w * 4w\)

\(= 2w^2 + w^2 + 6w^2 + 2w^2 = 11w^2\) ............. (2)

Area of shaded region \(= 25w^2 - 11w^2 = 14w^2\)

Fraction \(= \frac{14}{25}\)

Answer = B
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Re: In the square above, 12w = 3x = 4y. What fractional part of the square [#permalink] New post   Updated on: 10 Apr 2017, 11:31
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Bunuel wrote:

Tough and Tricky questions: Geometry.



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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

Kudos for a correct solution.

Take W=1 then
x=4
y=3

Area of 4 triangles= 11
Area of square =5^2=25
Portion shaded =25-11/25=14/25
Ans B

Originally posted by rohit8865 on 10 Jul 2016, 11:28.
Last edited by rohit8865 on 10 Apr 2017, 11:31, edited 1 time in total.
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Re: In the square above, 12w = 3x = 4y. What fractional part of the square [#permalink] New post   11 Jul 2016, 03:10
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area of shaded region = area of square-area of remaining bits
area of square = 25w^2
area of remaining bits = 1/2(2W^2+4w^2+4w^2+12w^2)=11W^2
area of shaded region = 25w^2-11w^2 =14w^2
fraction = 14/25
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Re: In the square above, 12w = 3x = 4y. What fractional part of the square [#permalink] New post   10 Apr 2017, 02:31
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Great question!
First we calculate total area of the square.
Then deduct sum of areas of 4 triangles.

Let's calculate areas in terms of w:

Area of the square = 5w * 5w = 25w^2
Sum of Area of 4 triangles = 1/2 * (2W^2+2*4w^2+12w^2)=11W^2

Area of the shaded region = 14w^2

Ratio = 14/25
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Re: In the square above, 12w = 3x = 4y. What fractional part of the square [#permalink] New post   09 Jul 2023, 20:57
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Re: In the square above, 12w = 3x = 4y. What fractional part of the square [#permalink]
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