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# The length of a rectangle is decreased by 15% and its width is increas

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The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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17 Jan 2016, 10:10
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Difficulty:

15% (low)

Question Stats:

83% (00:53) correct 18% (01:55) wrong based on 120 sessions

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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%

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The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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17 Jan 2016, 10:41
Let the length of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D.
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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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18 Jan 2016, 23:35
Hi All,

This question can be solved in a variety of different ways, including various algebraic approaches and TESTing VALUES. Here's how you can use fractions to your advantage and save some time.

We're told that the length of a rectangle is decreased by 15% and its width is increased by 40%. We're asked if the area of the rectangle decreases or increases and by what percent.

The original area of the rectangle can be written as...

(L)(W) = Area

The two changes can be written as:
15% decrease = 8.5/10
40% increase = 14/10

After the changes occur, we have...

(8.5/10)(L)(14/10)(W) =
(8.5/10)(14/10)(L)(W) =
(8.5)(14)/100 x (L)(W) =
119/100 x (L)(W)

119/100 = a 19% increase

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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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13 May 2017, 09:07
1
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.
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The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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13 May 2017, 12:59
1
asfandabid wrote:
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.

asfandabid, this shortcut looks handy. Clearly it's a percent change formula, but its elements and operations in the numerator aren't clear to me.

(Yes, I see that you've taken Change 1 of a side, added Change 2 of another side, then added the product of the two. Why? I'm having a hard time wrapping my mind around the idea that you would account separately for each one-dimensional change, add them, then account for a two-dimensional change, and add that on. And are you assuming original values of 100 per side?)

Please explain the formula? Perhaps you could write out the elements in the numerator and explain why the operators work as they do? Thanks in advance.
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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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16 May 2017, 00:40
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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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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16 May 2017, 02:29
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%

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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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16 May 2017, 03:28
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.

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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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16 May 2017, 11:19
1
Bunuel wrote:
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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The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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16 May 2017, 20:05
Abhishek009 wrote:
Bunuel wrote:
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
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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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19 May 2017, 06:19
Bunuel wrote:
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.

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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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13 Jun 2018, 03:36
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