The figure shown above represents a modern painting that consists of f

Question

https://gmatclub.com/forum/download/file.php?id=28116 The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length l and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles? (A) 15 (B) 20 (C) 25 (D) 30 (E) 40 2015-10-19_0007.png

ScottTargetTestPrep · Accepted Answer

Let’s begin by sketching the given diagram. We can also add in the appropriate dimensions to each side.

https://i.imgur.com/qjV9s0U.png

From the diagram we can create an equation:

l = w + w + w

l= 3w

We also know that the area is 4,800 square inches. Using the dimensions from our diagram and the formula for the area of a rectangle, we can say:

l(w + l) = 4,800

Since l = 3w, we can substitute 3w for l in the area equation l(w + l) = 4,800. Thus, we have:

3w(w + 3w) = 4,800

3w(4w) = 4,800

12w^2 = 4,800

w^2 = 400

w = ±20

Because we are dealing with a measurement, we disregard w = -20 as a solution. Thus, the width of each rectangle is 20 inches.

Answer: B

camlan1990 · Answer

As shown in Figure, l = 3w

The area of each small rectangle = l*w = 4,800/4 = 12*100

=> 3w*w = 12*100

=> w = 20

Ans: B

v12345 · Answer

we have l = 3w

so area of rectangle = l * (l + w) = 4800
=> 3w ( 3w + w) = 4800
=> 12 w^2 = 4800
=> w^2 = 400
=> w = 20 (taking +ve value)

Answer choice B

rhine29388 · Answer

from the figure we can see that l = 3w
4 rectangles have a combined area 4lw = 4800
therefore lw=1200
substituting l = 3w in above equation
3w^2=1200
w^2 = 400
taking positive square roots
w= 20

answer - B

GMATinsight · Answer

Observation 1: ℓ = 3w
Observation 2: ℓ*(ℓ+w) = 4800

i.e. 3w*(3w+w) = 4800

i.e. 12w^2 = 4800

i.e. w^2 = 400

i.e. w = 20 and ℓ = 60

Answer: Option B

andreroma · Answer

how can you say that l=3w?

rhine29388 · Answer

As you can see from the figure 3 small rectangles stacked in a linear fashion (horizontal ones where length appears to be bigger)
3 small widths = 3w (addition of three widths of the 3 above mentioned rectangles)
As can be figured out from the larger rectangle the addition of 3 smaller widths correspond to length of the remaining smaller rectangle
Therefore l=3w can be deduced

Hope the explaination helps
+1 kudos if you like it

gracie · Answer

equation 1: (l+w)(3w)=4800
equation 2: 4lw=4800➡l=1200/w
substituting for l in equation 1,
(1200/w+w)(3w)=4800
w=20

stonecold · Answer

This is a great question...One of the best questions in the official guide ..
Here => area => l^2+lw =4800 and l=3w => 12w^2 =4800 => w=20.
hence B

glt13 · Answer

Good stuff, gotta recognize a simple pattern here to solve in 30 seconds

the image shows you that l=3w

given, A of all = 4800. 4 pieces of equal length means then that lw = 1200

l=3w
lw=1200
3w(w)=1200
3w^2 = 1200
w^2 = 400
w=20 (cannot be -20, we are in feasibility mode here)

adkikani · Answer

Bunuel   Engr2012   shashankism

Can you help to understand flaw in below approach:
it is clear that the figure consists of one vertical rectangle and three horizontal rectangles.

Step 1: for all three horizontal rectangles area = 3 (l * w)
Step 2: for one vertical rectangles area = l*w

so total area of figure = 4 l* w (summation of above steps) which is given as 4800 as per Q stem.

We need two variables or need to express l / w in terms of another. Here is where I got stuck and could not proceed.

WR,
Arpit

unraveled · Answer

adkikani 
The other variable is (l+w)*l = 4800 which is total area given. OR (l+w)*3w = 4800
From there on you can solve for l and w both.

Also note that 3 horizontal areas form 1 square as 3w = l. So 1 vertical rectangle is  \frac{1}{4}^{th}  of the total area i.e. l*w =  \frac{4800}{4}  = 1200 as you have also done it.

TheUltimateWinner · Answer

E  is the trap answer. For  E  the length is 120. So the area is 40*120= 4800 , which is the area of the whole painting, but we need width of each of the four rectangles, which is B (20).
Hope it helps...

MHIKER · Answer

The length  l  of the table is equal to the width  (w)  of the small rectangle,  l=3w

Width of the large table  =3w+w=4w

Area of the large table  =3w*4w=12w^2

Given,  12w^2=4800

w^2=400

w=20

The answer is  B

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=E83g5QLJff4

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=nbogkfJq6HQ

100mitra · Answer

Correct option : B (20)
(LxW) x 4 = 4800 --- for all 4 rectangle 
LxW = 1200 ------(1)
L=3W
3W^2 = 1200
W^2 = 400
W=(20,-20) ---(2) taking positive 
 L = 20x3 = 60

KarishmaB · Answer

There are two ways to calculate the area of the entire painting:

Area of the entire painting = 4 * area of each rectangle = 4 * lw = 4800
This means lw = 1200

Area of the entire painting is also given by:   l * (l + w) = l^2 + lw = 4800

Since lw = 1200, 
 l^2 = 4800 - 1200 = 3600
l = 60
w = 1200/l = 1200/60 = 20

Answer (B)

yannichc · Answer

Can be solved using common sense

60*80=4800

3W= 60

W= 20

The figure shown above represents a modern painting that consists of f

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The figure shown above represents a modern painting that consists of f

Prep Toolkit

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