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23 Nov 2021, 06:44
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Rectangle given above is divided into eight squares. If the area of the yellow square in the center is 1, what is the area of the rectangle ?
A. \(14.5\)
B. \(29\)
C. \(40\)
D. \(41\)
E. \(58\)
23 Nov 2021, 06:44
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Official Solution:
Rectangle given above is divided into eight squares. If the area of the yellow square in the center is 1, what is the area of the rectangle ?
A. \(14.5\)
B. \(29\)
C. \(40\)
D. \(41\)
E. \(58\)
Say the side length of a red square in \(x\). Then:
The side length of a green square will be \(x+x=2x\);
The side length of a pink square will be \(x+x+1=2x+1\);
The side length of a purple square will be \((2x+1)+1=2x+2\);
The side length of a blue square will be \(2x+x-1=3x-1\).
Next, the length of the rectangle if we measure top side will be \((2x+1)+(2x+2)=4x+3\) and if we measure bottom side it will be \(2x+(3x-1)+(3x-1)=8x-2\). Equate:
Equate: \(4x+3=8x-2\). Solve: \(x=\frac{5}{4}\).
The area of the rectangle = \((4x+3)(5x+1)=58\).
Note: The area of a square, rectangle, the volume of a cube or a rectangular solid, and the Pythagorean theorem are not considered by the GMAT as specific geometry knowledge and can still be tested on the exam. There are several questions involving this in the GMAT Prep Focus mocks. Thus, the question above is not about geometry; it's rather on algebra.
Answer: E
Rectangle given above is divided into eight squares. If the area of the yellow square in the center is 1, what is the area of the rectangle ?
A. \(14.5\)
B. \(29\)
C. \(40\)
D. \(41\)
E. \(58\)
Say the side length of a red square in \(x\). Then:
The side length of a green square will be \(x+x=2x\);
The side length of a pink square will be \(x+x+1=2x+1\);
The side length of a purple square will be \((2x+1)+1=2x+2\);
The side length of a blue square will be \(2x+x-1=3x-1\).
Next, the length of the rectangle if we measure top side will be \((2x+1)+(2x+2)=4x+3\) and if we measure bottom side it will be \(2x+(3x-1)+(3x-1)=8x-2\). Equate:
Equate: \(4x+3=8x-2\). Solve: \(x=\frac{5}{4}\).
The area of the rectangle = \((4x+3)(5x+1)=58\).
Note: The area of a square, rectangle, the volume of a cube or a rectangular solid, and the Pythagorean theorem are not considered by the GMAT as specific geometry knowledge and can still be tested on the exam. There are several questions involving this in the GMAT Prep Focus mocks. Thus, the question above is not about geometry; it's rather on algebra.
Answer: E
