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The length of a rectangle is decreased by 15% and its width is increas [#permalink]
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Question Stats: Hide Show timer StatisticsThe 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] Let the length of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xyNow 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] 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) = AreaThe two changes can be written as:15% decrease = 8.5/1040% increase = 14/10After 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 Final Answer: GMAT assassins aren't born, they're made,Rich _________________
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Re: The length of a rectangle is decreased by 15% and its width is increas [#permalink] We can also solve this by using the formulaa+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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Re: The length of a rectangle is decreased by 15% and its width is increas [#permalink] Let the original length be 20 ; and width = 10 original area = 20 * 10 = 200New length = .85 * 20 = 17New width = 1.40 * 10 = 14new 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] Let original length= L; original width= WNew length= 0.85L; New width= 1.4WOriginal Area= LWNew Area= 0.85L*1.4W= 1.19LWChange in Area= 1.19LW-LW= 0.19LWPercentage increase= \(\frac{0.19LW}{LW}\)*100= 19%Answer: D. Kudos please if you like my explanation!
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Re: The length of a rectangle is decreased by 15% and its width is increas [#permalink] 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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Re: The length of a rectangle is decreased by 15% and its width is increas [#permalink]
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]
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 % ?thanksAbhijeet
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Re: The length of a rectangle is decreased by 15% and its width is increas [#permalink]
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.Answer: D _________________
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Re: The length of a rectangle is decreased by 15% and its width is increas [#permalink] Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: The length of a rectangle is decreased by 15% and its width is increas [#permalink] 13 Jun 2018, 02:36 |
What will be the change in area of a rectangle if its length is increased by 15% and no change in breadth?
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