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A gardener increased the length of his rectangle-shaped garden by 40

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A gardener increased the length of his rectangle-shaped garden by 40  [#permalink]

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New post 03 Dec 2014, 08:15
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A
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Tough and Tricky questions: Geometry.



A gardener increased the length of his rectangle-shaped garden by 40 percent and decreased its width by 20 percent. The area of the new garden

A) has increased by 20 percent
B) has increased by 12 percent
C) has increased by 8 percent
D) is exactly the same as the old area
E) cannot be expressed in percentage terms without actual numbers

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: A gardener increased the length of his rectangle-shaped garden by 40  [#permalink]

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New post 03 Dec 2014, 09:24
1
Bunuel wrote:

Tough and Tricky questions: Geometry.



A gardener increased the length of his rectangle-shaped garden by 40 percent and decreased its width by 20 percent. The area of the new garden

A) has increased by 20 percent
B) has increased by 12 percent
C) has increased by 8 percent
D) is exactly the same as the old area
E) cannot be expressed in percentage terms without actual numbers

Kudos for a correct solution.

Source: Chili Hot GMAT


The quickest way I found to do this problem was just to plug in some numbers and test. Taking a 10x2 rectangle of area 20, increasing the length 40% and decreasing the width 20% gives us a 14x1.6 rectangle with area 112. So the answer is (B) 12%.
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Re: A gardener increased the length of his rectangle-shaped garden by 40  [#permalink]

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New post 03 Dec 2014, 12:24
Let the original area be a=l*w (where l and w are the length and width of the original garden, respectively)
The new area is then a'=1.4*l*0.8*w = 1.12*l*w
The new area is 1.12 times the original area or an increase of 12%.

Choice B
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Re: A gardener increased the length of his rectangle-shaped garden by 40  [#permalink]

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New post 03 Dec 2014, 21:09
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Answer = B) has increased by 12 percent

Please note that every SQUARE IS A RECTANGLE; so taking choicest values for ease in calculation :)

Original Garden

Length = 10

Width = 10

Area = 100

Modified Garden

Length = 10+4 = 14

Width = 10-2 = 8

Area = 112

Increase in percentage \(= 112-100 = 11.2 \approx{12}\)
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Re: A gardener increased the length of his rectangle-shaped garden by 40  [#permalink]

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New post 03 Dec 2014, 22:56
Let x & y be original length and width.
original area = x*y

modified length = 1.4x
modified width = 0.8y
modified area = 1.4x*0.8y = 1.12xy = 12% increase

Ans. B) has increased by 12 percent
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Re: A gardener increased the length of his rectangle-shaped garden by 40  [#permalink]

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New post 04 Dec 2014, 07:29
Bunuel wrote:

Tough and Tricky questions: Geometry.



A gardener increased the length of his rectangle-shaped garden by 40 percent and decreased its width by 20 percent. The area of the new garden

A) has increased by 20 percent
B) has increased by 12 percent
C) has increased by 8 percent
D) is exactly the same as the old area
E) cannot be expressed in percentage terms without actual numbers

Kudos for a correct solution.

Source: Chili Hot GMAT


The correct answer is B.
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Re: A gardener increased the length of his rectangle-shaped garden by 40  [#permalink]

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New post 02 Jul 2017, 06:47
1
I guess the fastest way to solve this type of question is by using successive percentage increase and decrease.

The Effective percentage for successive increase/decrease is give by \(A + B + \frac{AB}{100}\)

So, the effective incrase in this question is \(40 - 20 - \frac{40*20}{100} = 20 - 8 = 12\)%

Bunuel wrote:

Tough and Tricky questions: Geometry.



A gardener increased the length of his rectangle-shaped garden by 40 percent and decreased its width by 20 percent. The area of the new garden

A) has increased by 20 percent
B) has increased by 12 percent
C) has increased by 8 percent
D) is exactly the same as the old area
E) cannot be expressed in percentage terms without actual numbers

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: A gardener increased the length of his rectangle-shaped garden by 40   [#permalink] 02 Jul 2017, 06:47
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