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10 Nov 2014, 03:15
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
71% (02:53) correct
29%
(02:58)
wrong
based on 249
sessions
History
Date
Time
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Not Attempted Yet
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
Attachment:
1.gif [ 1.83 KiB | Viewed 8947 times ]
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
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
General Discussion
Bunuel
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
