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26 Sep 2017, 00:20
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
87% (01:43) correct
13%
(01:46)
wrong
based on 46
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In the square above, if the ten nonoverlapping regions have the areas as shown, which of the following is equal to y?
(A) x + t
(B) s + t
(C) a + s + t
(D) b + s + t
(E) a + b + s
Attachment:
2017-09-26_1116.png [ 6.87 KiB | Viewed 2209 times ]
26 Sep 2017, 01:58
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Bunuel
In the given figure, the square with area x^2 has length and width x each. So, for the rectangle with area xy on the left, the width is x and area is xy so length is y. Similarly, for the rectangle on the top with area xy, the length is x and area is xy so width is y. Therefore, the length/width of the square = x + y.
Area of the square = \((x+y)^2 = x^2 + 2xy + y^2\)
From the given figure, the area of the square is equal to the sum of the areas of the ten regions inside it.
So, \(x^2 + 2xy + y^2 = x^2 + 2xy + a^2 + 2ab + s^2 + st + st + t^2\)
On simplifying it, \(y^2 = a^2 + 2ab + (s+t)^2\)
\(y^2 = (a+b)^2 - b^2 + (s+t)^2\)--------- equation 1
Similar to how the outside square's length was found out, we can see in the inside figure has length of side a+b.
Its area = \((a+b)^2\)= sum of the areas of the constituting regions inside
So, \((a+b)^2 = a^2 + 2ab + s^2 + 2st + t^2\)
On simplifying it, \(b^2 = (s+t)^2\)----------- equation 2
Using this in equation 1,
\(y^2 = (a+b)^2\)
y = a+b (since they are non-negative)
Since b = s+t from equation 2 (since they are non-negative), y = a+b = a + s + t
Therefore, the answer is C.
26 Sep 2017, 03:24
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Attachment:
2017-09-26_1116.png [ 8.33 KiB | Viewed 2014 times ]
From Square 1, we know that side = x
From Rectangle 2, we know length = y as breadth is the same as the side of the square(x)
From Square 3, we know that side = a
From Rectangle 4, we know length = b as breadth is the same as the side of the square(a)
From Square 5, we know that side = s
From Rectangle 2, we know length = t as breadth is the same as the side of the square(s)
Taking Rectangle 2, Square 3, and Rectangle 4,
we know that the length of Rectangle 2 is equal to sum of side of Square 3 and length of Rectangle 4
y = a + b -> (1)
Similarly taking Rectangle 4, Square 5, and Rectangle 6,
we know that the length of Rectangle 4 is equal to sum of side of Square 5 and length of Rectangle 6
b = s + t -> (2)
Substituting (2) in equation (1), we get the value of y = a + s + t(Option C)
