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Bunuel
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We can also solve this by using the formula

a+b+(a*b)/100
=(-15)+(40)+(-15*40)/100
=25-6
=19%
which is positive so it represents a 19% increase.
D is the answer
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Let the original length be 20 ; and width = 10
original area = 20 * 10 = 200

New length = .85 * 20 = 17
New width = 1.40 * 10 = 14

new area = 17 * 14 = 238

% increase =\(\frac{38}{200} * 100\) = 19%

Ans: D
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Let original length= L; original width= W
New length= 0.85L; New width= 1.4W

Original Area= LW
New Area= 0.85L*1.4W= 1.19LW

Change in Area= 1.19LW-LW= 0.19LW
Percentage increase= \(\frac{0.19LW}{LW}\)*100= 19%

Answer: D.

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Simplest Way:-
New Length : 0.85L (L= Original length)
New Width : 1.4W (L= Original width)
Therefore New Area= 0.85*1.4*L*W=1.19LW implies 19%Increase.

Sent from my HM NOTE 1S using GMAT Club Forum mobile app
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Bunuel
The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%

\(-15 + 40 +\frac{(-15)(40)}{100}\)

\(= 25 - 6\)

\(= 19\)

Thus, there will be an increase in area by (D) 19%
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Abhishek009
Bunuel
The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%

\(-15 + 40 +\frac{(-15)(40)}{100}\)

\(= 25 - 6\)

\(= 19\)

Thus, there will be an increase in area by (D) 19%


Hi Abhishek,

Please explain above approach. Is this approach applicable for all % increase or % decrease problems ?

How will you identify that 19 is increase or decrease % ?

thanks
Abhijeet
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Bunuel
The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%

We can let the original length of the rectangle = x and the original width of the rectangle = y. Thus, the original area is xy.

When the length decreases by 15%, the new length is 0.85x, and when the width increases by 40%, the new width is 1.4y. Thus, the new area is (0.85x)(1.4y) = 1.19xy.

We can use the percent change formula: (New Value - Old Value)/Old Value x 100%. Thus, the area changes by (1.19xy - xy)/xy = 0.19xy/xy = 0.19 = 19%. This value is positive, indicating an increase.

Answer: D
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