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# What is the area of the shaded quadrilateral in the figure above?

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Intern
Joined: 02 Mar 2016
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27 Feb 2017, 13:13
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Difficulty:

5% (low)

Question Stats:

84% (01:10) correct 16% (01:32) wrong based on 110 sessions

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What is the area of the shaded quadrilateral in the figure above?

(1) a^2 − b^2 = 40

(2) a^2 + b^2 = 58

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Intern
Joined: 07 Jul 2016
Posts: 12
GMAT 1: 700 Q47 V39
GPA: 3.38

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27 Feb 2017, 16:20
Would appreciate other people's feedback on Statement 1, but came about it as follows:

1) X^2 - Y^2 = 40

Even after breaking down into (x+y) * (x-y) = 40, didn't seem to help much. Left it as insufficient.

2) X^2 + Y^2 = 58

Using the pythagorean theorem, broke it down into a^2 + b^2 = c^2. Therefore, c^2 = 58, which is the area of the quadrilateral. Accordingly, B is sufficient.
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28 Feb 2017, 06:54
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Matruco wrote:
What is the area of the shaded quadrilateral in the figure above?

(1) a^2 − b^2 = 40

(2) a^2 + b^2 = 58

The area of the big square is $$(a+b)^2$$

The area of each triangle is $$\frac{ab}{2}$$

$$(a+b)^2-4 \times \frac{ab}{2}=a^2+b^2$$

(1) $$a^2-b^2=40$$. We can't know what the value of $$a^2+b^2$$ is. Insufficient.

(2) It's clear that $$a^2 + b^2 = 58$$ is the area of the shaded quadrilateral . Sufficient.

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13 Mar 2017, 14:15
In order to solve this question, we need to know the lengths of the hypotenuses of the triangles. I think.

What is the area of the shaded quadrilateral in the figure above?

(1) a^2 − b^2 = 40

(2) a^2 + b^2 = 58

Statement (1) gives us two variables, meaning we cannot solve the equation. We cannot extrapolate a hypotenuse length from this equation either. Insufficient.

Statement (2) allows us to determine what the length of side C is by squaring 58. Sufficient.
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15 Mar 2017, 05:24
St 1: a^2-b^2 = 40
or (a+b)(a-b) = 40
number of cases possible. INSUFFICIENT

St 2: a^2 +b^2 = 58.
for each side if the shaded quadrilateral, we can say that a^2 +b^2 = c^2
therefore the shaded region is a square with side c and the area c^2 = 58. ANSWER

Option B
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07 Nov 2017, 09:49
Area of the shaded region = Area of square - (sum of all areas of triangles)
$$= (a+b)^2 - 4* [ \frac{1}{2} * a * b]$$ ; if you notice area of each triangle is the same $$= \frac{1}{2} *a * b$$
$$= (a+b)^2 - 2ab$$
$$= a^2 + b^2 + 2ab - 2ab$$
$$= a^2 + b^2$$

Statement 1 : Not sufficient.

Statement 2: gives us the direct value of $$a^2 + b^2$$
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Re: What is the area of the shaded quadrilateral in the figure above? &nbs [#permalink] 07 Nov 2017, 09:49
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