The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, P, Q, R, and S.

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Source: GMAT Paper Tests
AreaGeometry.PNG
The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, P, Q, R, and S. In square meters, the area of square region Q is x^2, the area of rectangular region R is 5x, and the area of rectangular region P is 4x. What is the area, in square meters, of rectangular region S?

A. \(x^2-x\)
B. \(x^2+9x\)
C. \(20x-x^2\)
D. \(9\)
E. \(20\)

The OA is E

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BTGmoderatorLU wrote:
Sat Jul 24, 2021 5:00 pm
Source: GMAT Paper Tests

AreaGeometry.PNG

The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, P, Q, R, and S. In square meters, the area of square region Q is x^2, the area of rectangular region R is 5x, and the area of rectangular region P is 4x. What is the area, in square meters, of rectangular region S?

A. \(x^2-x\)
B. \(x^2+9x\)
C. \(20x-x^2\)
D. \(9\)
E. \(20\)

The OA is E
Area of \(Q = x^2\); Side \(= x\)
Area of \(R = 5x = x \ast \) length; length of \(R = 5\)
Area of \(P = 4x = x \ast \) width; width of \(P = 4\)

Area of the entire plot \(=(x+4)\ast (x+5)=x^2+9x+20\)

Area of \(S=x^2+9x+20-x^2-5x-4x=20\)

Therefore, E