GMAT CLUB OLYMPICS: Rectangle given above is divided into eight square

Question

https://gmatclub.com/forum/download/file.php?id=62919 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 M37-35 Untitled9.png

Bunuel · Accepted Answer

Official Solution:

https://gmatclub.com/tests-beta/resources/import/img/M37-35.png 
 
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

https://gmatclub.com/tests-beta/resources/import/img/M37-35-2.png 
 
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 .

Answer: E

Kinshook · Answer

https://gmatclub.com/forum/download/file.php?id=62919 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 ? Screenshot 2021-08-19 at 9.12.49 PM.png Length of the rectangle = 2(4-y) + 1 + 2y - 1 = 8 - 2y + 1 + 2y - 1 = 8 = (2y-1) + (2y-2) = 4y - 3 y = 11/4 = 2.75 Width of the rectangle = y + (2y-1) = 3y- 1 = 33/4 -1 = 7.25 Area of the rectangle = 8*7.25 = 58 IMO E

andreagonzalez2k · Answer

Let be:
b: side of the small square to the left of the square of side 1.

We can deduce the dimensions of the rectangle:
 left side = 5b + 1 
 botton side = 4b + 3 
 right side = 3b + \frac{7}{2}

As left side must be equal to right side:
 5b + 1 = 3b + \frac{7}{2}  ->  b = \frac{5}{4}

Area of rectangle:
 (5b + 1)(4b + 3) = \frac{29}{4} * 8 = 58

IMO E

SohGMAT2020 · Answer

If we look at the attached figure.

Let AB = x ;

On the basis of properties of square, other side dimensions in term of x are given

Now let consider the shaded square,

one side comes to 2x -3, but the other one comes to 8 - 2x .

Since both are equal,

2x - 3 = 8 - 2x

or 4x = 11
or x = 11/4

Area = ( 4x -3) (3x - 1)
 = ( 11 -3) ( 33/4 - 1)
 = 8 * 7.25
 = 58
 So option E is correct

captain0612 · Answer

Q : Rectangle given above is divided into eight square

Answer : E

if we divide the total rectangle as shown in the figure,
we end with the equation :
(6 + 5x)(7 + 4x) , since area of rectangle = (length)*(breadth)

and here length = 7 + 2x
breadth = 6 + 4x 
where x >0

solving the equation gives us : 42 + 20x^2 + 79x, which is always greater than 42 and hence only option greater than 42 is E

#Geometry
#Quant
#700

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GMAT CLUB OLYMPICS: Rectangle given above is divided into eight square

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