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The length of a rectangle is 3 inches, plus or min
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30 Jul 2017, 08:44

2

Expert Reply

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Question Stats:

The length of a rectangle is 3 inches, plus or minus an amount no greater than \(\frac{1}{2}\) inch while its width is 2 inches, plus or minus an amount no greater than \(\frac{1}{4}\) inch. Which of the following could be the percentage by which the actual area of the rectangle is greater than or less than its nominal area of 6 square inches?

Indicate all that apply.

❑ -30%

❑ -25%

❑ +25%

❑ +30%

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
20 Apr 2019, 01:59

6

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.

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.

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
10 Dec 2019, 07:45

any other explanation?

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
10 Dec 2019, 07:50

Expert Reply

The above is the simplest way to solve it.

Possible other solutions would become cumbersome.

Regards

Possible other solutions would become cumbersome.

Regards

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
24 Apr 2020, 02:40

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

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
24 Apr 2020, 06:06

Expert Reply

Thank you Sir for the explanation

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
27 Jul 2020, 02:29

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.

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?

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
27 Jul 2020, 04:37

Expert Reply

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

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

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
27 Jul 2020, 07:14

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

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

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
27 Jul 2020, 08:02

1

Expert Reply

In fact, the % change is what the question is asking you but it is not clearly stated. it is an inference reading it

Re: The length of a rectangle is 3 inches, plus or min
[#permalink]
12 Apr 2023, 06:25

1

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.

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.

Re: The length of a rectangle is 3 inches, plus or min
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16 Apr 2024, 12:35

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Re: The length of a rectangle is 3 inches, plus or min [#permalink]

16 Apr 2024, 12:35
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