M37-32

Question

https://gmatclub.com/gmat-practice-tests/resources/import/img/M37-32.png 
 
A square shown above is divided into 5 rectangles, each having the same area. If the upper left rectangle has a width of 5 units, then what is the area of the square?

A.  100 
B.  169 
C.  225 
D.  400 
E.  625

Bunuel · Answer

Official Solution:

https://gmatclub.com/gmat-practice-tests/resources/import/img/M37-32.png 
 
A square shown above is divided into 5 rectangles, each having the same area. If the upper left rectangle has a width of 5 units, then what is the area of the square?

A.  100 
B.  169 
C.  225 
D.  400 
E.  625

https://gmatclub.com/gmat-practice-tests/resources/import/img/M37-32-2.png 
 
Say the length of the purple rectangle is  x . Then the area of all 5 rectangles will be  5x .
 
Say the length of the red rectangle is  y . Then the combined area of red, yellow, and green rectangles will be  xy , as well as  5x+5x+5x=15x . 
 
So,  xy=15x . This gives:  y=15 .
 
The side of the square is  5+y=20  and the area is  20^2=400 .
 
Note that while this question uses basic knowledge of lines and figures, it is actually not a Geometry question. There are 8 questions within GMAT Prep Focus Edition that use similar principles.  Here is one example .

Answer: D

punit2020 · Answer

side of square = a
area of each rectangle = a^2 / 5
area of violet rectangle = 5*x = a^2 / 5
x = a^2 / 5^2
horizontal side of blue rectangle = a/5
upper horizontal side of square = (a^2 / 5^2) + a/5 = a (solving gives a = 20)
area = 400

AaryanGupta1200 · Answer

This is a great question that’s helpful for learning.

Rebaz · Answer

I am in awe of this question's Complexity and at the same time of the simplicity with which  Bunuel  has solved it.

Great Questtion!

Thanks!

agrasan · Answer

I like the solution - it’s helpful.

nihilveritatis · Answer

I thought of this as a factors question.

We know the square is divided into 5 rectangles with the same areas. Essentially, we need a number that when divided by 5 results in such a number that can be found by multiplying four unique number pairings as we can see 2 identical rectangles and rest unique.

I saw that all options can be divided by 5 and 400 seemed the best option for the above condition.

400/5 = 80

80 gives us 4 unique pairings (5,16) (10,8) (4,20) (2,40)

Looking at the solution i think i may have gotten the right answer using the wrong way

M37-32

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