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If a square with 20 as one side’s length and decreases to

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If a square with 20 as one side’s length and decreases to

by AAPL » Wed Aug 01, 2018 6:11 am

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If a square with 20 as one side's length and decreases to a and b shown as above figure, what is the area of the region shaded?

1) (a+b)^2=49
2) (a^2)+(b^2)=25

The OA is B.

Area of square = 20^2 = 400
Area of top triangle enclosed by the length a = 0.5 * a^2
Area of the bottom triangle enclosed by length b = 0.5 * b^2
Area of shaded region = 400 - 0.5(a^2 + b^2)

Statement 1: (a + b)^2 = 49 --> a^2 + b^2 + 2ab = 49 --> Not sufficient as we do not know the value of 2ab

Statement 2: Clearly sufficient.

Therefore, B is the correct answer.
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by deloitte247 » Sat Aug 18, 2018 3:12 pm

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Question : What is the area of the shaded region?
$$Area\ of\ square\ =\ 20^2\ =\ 20\ \cdot\ 20\ =\ 400$$
$$Area\ of\ top\ traingle\ enclosed\ by\ lenght\ a\ =\ 0.5\ \cdot\ a^2$$
$$Area\ of\ bottom\ traingle\ enclosed\ by\ lenght\ b\ =\ 0.5\ \cdot\ b^2$$
$$Area\ of\ shaded\ region\ =\ 400\ -\ 0.5\ \left(a^2\ +\ b^2\right)$$
$$Statement\ 1\ =\ \left(a\ +\ b\right)^2\ =\ 49$$
$$Therefore,\ \ a^2\ +\ b^2\ +\ 2ab\ =\ 49$$
We don't know the value of 2ab,
Hence statement 1 is NOT SUFFICIENT.

$$Statement\ 2\ :\ \ \left(a^2\right)\ +\ \left(b^2\right)=\ 25$$
$$Area\ of\ shaded\ region\ =\ 400\ -\ 0.5\ \left(a^2\ +\ b^2\right)$$
= 400 - 0.5 (25)
= 400 - 12.5
= 383

Hence, statement 2 is SUFFICIENT.
Option B is CORRECT.
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