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In the square above, 12w = 3x = 4y. What fractional part of the square
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10 Nov 2022, 10:34
10 Nov 2022, 10:34
Expert Reply
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Question Stats:
50% (03:21) correct
50% (04:00) wrong based on 8 sessions
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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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Re: In the square above, 12w = 3x = 4y. What fractional part of the square
[#permalink]
14 Nov 2022, 07:52
14 Nov 2022, 07:52
1
Expert Reply
12w = 3x = 4y
x = 4w &
y = 3w
Area of square \(= (5w)^2 = 25w^2\) .............. (1)
Area of unshaded 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
x = 4w &
y = 3w
Area of square \(= (5w)^2 = 25w^2\) .............. (1)
Area of unshaded 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
gmatclubot
Re: In the square above, 12w = 3x = 4y. What fractional part of the square [#permalink]
14 Nov 2022, 07:52
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