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If the length and width of a rectangular garden plot were ea

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

Problem Solving
Question: 89
Category: Geometry Area
Page: 73
Difficulty: 600


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SOLUTION

If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

Original area = LW;
New area = (1.2L)(1.2W) = 1.44LW.

The percent increase = 44%.

Answer: E.
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Re: If the length and width of a rectangular garden plot were ea [#permalink]

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Let initial length and width be l and w respectively.

Initial area = lw

New length = (6/5) l
New width = (6/5) w

New area = (36/25) lw or 144%.

Hence, increase of 44%

Answer (E).

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Re: If the length and width of a rectangular garden plot were ea [#permalink]

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New post 12 Feb 2014, 05:49
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The quickest way to do this is to pick numbers: l = 10 & w = 10;
Note: Both l & w can be same as a square is also a rectangle.

Original area = lw =10 * 10 = 100;

Since l & w are increased by 20% each, l & w = 12;
New area = lw = 12 * 12 = 144;

% increase in area = 144 - 100 = 44%.

Ans is (E).

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Re: If the length and width of a rectangular garden plot were ea [#permalink]

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New post 12 Feb 2014, 07:09
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My method might seem long but once you get a hang of it, it seems easier.


Whenever we are asked to "increase" any quantity by some precentage value. Add that value with 100 and then perform the operations.

As in this case the sides are increased by 20%
By adding 20 to 100 we will get 120%
Both the sides are increased by 20% , therefore we have l=120% and b=120%

We have to find the area, formula for the area is l*b = 120%*120% = 14400 = 14400/100 = 144%

Remove the original 100 back to get 44%

Remember when we say 120 percent length, it means 100% of original length + 20% is the increament



You can use it with decimal too.
suppose l = x and b = y
Area = xy
New l2 = 1.2x (Why 1.2? becasuse original was 1x and it increased by 20% which is 0.2)
b2 = 1.2y
Area = 1.2x *1.2y = 1.44 xy

Last edited by b2bt on 15 Feb 2014, 07:57, edited 1 time in total.

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Re: If the length and width of a rectangular garden plot were ea [#permalink]

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New post 15 Feb 2014, 07:08
SOLUTION

If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

Original area = LW;
New area = (1.2L)(1.2W) = 1.44LW.

The percent increase = 44%.

Answer: E.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If the length and width of a rectangular garden plot were ea [#permalink]

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New post 26 Apr 2016, 13:51
Consider length of rectangle be L and width be W
original area = L * W
increased length = 1.2 L
increased width = 1.2 W
new area = 1.2 L * 1.2 W = 1.44 LW
Clearly a 44% increase in area
correct answer - E

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Re: If the length and width of a rectangular garden plot were ea [#permalink]

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New post 02 Jun 2017, 09:00
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

Problem Solving
Question: 89
Category: Geometry Area
Page: 73
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


You can also use real numbers to make the problem more concrete.

Original
L = 5
W = 10
A = 50

New
L = 6
W = 12
A = 72

72/50 -1 = 22/50 = 44/100 = 44%

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Re: If the length and width of a rectangular garden plot were ea [#permalink]

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New post 05 Jun 2017, 15:58
Bunuel wrote:

If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%


We can let the original area = lw, and thus the increased area is 1.2(l) x 1.2w = 1.44lw.

Thus, the percentage increase is:

(1.44lw - lw)/lw x 100

0.44lw/lw x 100 = 44%.

Answer: E
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If the length and width of a rectangular garden plot were ea [#permalink]

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This is also be solved by using the successive percentage increase approach. Here's why - Lets say the original area is a. When length and breath are increased by 20% it means we are successively increasing a by 20%.

If any number is successively increased by a% and then b%, the effective percentage increase is given by \(a + b + \frac{ab}{100}\)

In our case this becomes \(20 + 20 + \frac{20*20}{100} = 40 +4 = 44\)%

Answer choice E
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