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The length of a rectangle is 3 inches, plus or min : Multiple-choice Questions — Select One or More Answer Choices

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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
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The above is the simplest way to solve it.

Possible other solutions would become cumbersome.

Regards
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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
2
huda wrote:
any other explanation?


YES

1/2 is 1/6th of 3 which means 16.67%

1/4 is 1/8th of 2 which means 12.5%

Increasing/decreasing length and breadth is like successive percentage increase/decrease in area

So successive percentage increase of 16.67 and 12.5 can be an overall 30% increase

But successive percentage decrease of 16.67 and 12.5 will be an overall decrease less than 29%

So -30% is not possible
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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
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Thank you Sir for the explanation
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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
fifan wrote:
Consider the range of values that L and W of rectangle can take.

2.5<=L <=3.5
1.75<=W<=2.25
We can multiply L and w to get the range of rectangles area.

4.375 <=LW<=7.875

The minimum area can be 4.375 while the maximum area can be 7.875. take the two extremes and calculate how much each is greater or less than the nominal area 6. The area can be at most 27% less than 6 or at most 31% greater than 6. so the area can be between the range -27% to 31% we can see that -25% +25% and +31% fall in this range.


How did you calculate the percentage?
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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
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I am quite sure you do not read our quant book.

The % change is well explained here https://gre.myprepclub.com/forum/gre-quant ... tml#p52034

\(\frac{7.875-6}{6}=0.3125 \times 100 = 31.25\) which is \(\approx 31\)%

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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
Carcass wrote:
I am quite sure you do not read our quant book.

The % change is well explained here https://gre.myprepclub.com/forum/gre-quant ... tml#p52034

\(\frac{7.875-6}{6}=0.3125 \times 100 = 31.25\) which is \(\approx 31\)%

Regards


Oh ofcourse I did read all the chapters and percent change formula is easiest of all to remember. I didnt read this question correctly though that it is asking for percent change :(
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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
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In fact, the % change is what the question is asking you but it is not clearly stated. it is an inference reading it
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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
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We can answer this question by looking within the allowable ranges of percentage changes.


Largest possible area is the area with using the length and breadth with the highest possible values.

Highest possible Length, L = 3+(1/2) = 3.5
Highest possible Breadth, B = 2+(1/4) = 2.25

Max Area, A = LB = 3.5*2.25= 7.875

Highest percentage increase = ((7.875 - 6)*100)/6 = +31.25%


Smallest possible area is the area with using the length and breadth with the lowest possible values.

Lowest possible Length, L2 = 3-(1/2) = 2.5
Lowest possible Breadth, B2 = 2-(1/4) = 1.75

Min Area, A (min) = LB = 2.5*1.75 = 4.375

Highest percentage decrease = ((4.375 - 6)*100)/6 = -27.08%

Only options B, C, and D are in between -27.08% and +31.25% and are correct.
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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
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Re: The length of a rectangle is 3 inches, plus or min [#permalink]
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