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Does the area of a certain square greater than

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Source: — Data Sufficiency |
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by melguy » Sat Nov 19, 2016 9:30 pm
Statement 1

Square = 10 x 10 = 100
Rectangle = 10 x 5 = 50
or
Square = 10 x 10 = 100
Rectangle = 10 x 20 = 200

Not Sufficient

Statement 2

Square = 10 x 10 = 100
Rectangle = 20 x 1 = 20
or
Square = 10 x 10 = 100
Rectangle = 20 x 15 = 300

Not Sufficient

Combine

1 side is equal = 10 (for both)
1 side of the rectangle is twice the square (i.e. square = 10, Rectangle = 20)

We can say with certainty that the area of rectangle will be greater.

Answer is C
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by Jay@ManhattanReview » Tue Dec 06, 2016 2:20 am
Nandish,

A square can be called a special rectangle having equal length and breadth.

This question can be solved logically.

We know that the area of a rectangle = Length (a) * Breadth (b) = a*b

Clearly, statement 1 is insufficient as the area of the square = a^2. We cannot compare a^2 and a*b as we have no information about b.

Similarly, statement 2 is insufficient as we do not have any information about the other side of the rectangle: it may be equal to, greater than or smaller than that of the square, resulting in all possible results: Area is equal, more, and less.

However, combining both the statements will result in a unique answer.

Area of square = a^2;

Area of rectangle = a*(2a) = 2a^2 > a^2.

The answer is a unique 'NO'. OA C

Hope this helps!

--Jay

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