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A circular tabletop is to be cut from a square piece of wood

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Carcass
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A circular tabletop is to be cut from a square piece of wood [#permalink] New post   10 Dec 2019, 08:05
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#greprepclub A circular tabletop is to be cut.png
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A circular tabletop is to be cut from a square piece of wood as shown above.


Quantity A
Quantity B
Percent of the wood surface shown above that is not to be used for the tabletop
25%




A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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B
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A circular tabletop is to be cut from a square piece of wood [#permalink] New post   20 Apr 2022, 11:54
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Carcass wrote:
Attachment:
#greprepclub A circular tabletop is to be cut.png



A circular tabletop is to be cut from a square piece of wood as shown above.


Quantity A
Quantity B
Percent of the wood surface shown above that is not to be used for the tabletop
25%




Let's first assign a nice value to the radius of the circular table top.
Let's say the circular table top has a radius of 1
Image


This means the DIAMETER of the circle = 1 + 1 = 2
Image


This tells us that each side of the square piece of wood must have length 2
Image

Area of the circle \(= \pi (radius)^2 = \pi (1)^2 = \pi ≈ 3.14\)
Area of square \(= side^2 = 2^2 = 4\)

So, the AREA of the wood surface we'll be removing = 4 - 3.14 ≈ 0.86
So, to find the PERCENT of the wood we'll be removing, we must take 0.86/4 and convert it to a percent.
However, since we already know that 1/4 = 25%, we can be certain that 0.86/4 equals some value less than 25%

We have:
QUANTITY A: some value less than 25%
QUANTITY B: 25%

Answer: B
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Re: A circular tabletop is to be cut from a square piece of wood [#permalink] New post   14 Dec 2019, 02:56
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Let Side of square = a
Radius of circle = r --> a = 2r

area of square - area of circle
4r^2 - (pi)r^2 --> (pi = 3.14 approx)
= 0.86r^2 --> A

25% of area of square = (1/4)4r^2 = r^2 --> B

B is greater. Hence, B is the Answer.
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Re: A circular tabletop is to be cut from a square piece of wood [#permalink] New post   16 Sep 2021, 22:36
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Method:

Consider r = 2 . Hence diameter = side of the square = 4.
Area of circle = 4 pi
Area of square = 16 .

Area of unused cloth = 16 - 4 pi = 3.43

% Percentage of unused cloth = Area of unused cloth / Area of square

= 21 %

QA = 21 % < QB
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Re: A circular tabletop is to be cut from a square piece of wood [#permalink] New post   18 Sep 2021, 05:37
Can someone comment on the method that i have used and let me know if its correct here? :(
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Re: A circular tabletop is to be cut from a square piece of wood [#permalink] New post   18 Sep 2021, 08:52
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It's correct :thumbsup:
aishumurali wrote:
Can someone comment on the method that i have used and let me know if its correct here? :(
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Re: A circular tabletop is to be cut from a square piece of wood [#permalink] New post   20 Apr 2022, 11:18
Can someone help me with a simple, logic-based answer to this question, please? The math is too confusing. :(
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A circular tabletop is to be cut from a square piece of wood [#permalink] New post   20 Apr 2022, 11:41
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Attachment:
#greprepclub A circular tabletop is to be cut.png
#greprepclub A circular tabletop is to be cut.png [ 12.13 KiB | Viewed 4429 times ]


When you see a figure like this the first trick is always to have in mind that the diameter of the circle is always equal the side of the square

See the two red vertical lines. The question is asking basically what % of the purple areas (four corners) are the entire square area

Pick a number

the diameter of the circle is 4 >>>> so the side of the square is 4. area = s^2=16

Now area of the entire square which is 16 LESS the area of the circle which is \( 4 \pi\) = 4*3.14 = 12.56

Area of the square minus the area of the circle = 16-12.56 = 3.44

This value is the purple area I have highlighted

Now a touch of translation of words into math

What % 3.44 is the entire area of the square

Tranlsation

\(3.44=\frac{x}{100}*16\)

Find x which is \(\approx 21.43\)

21.43 < 25 %

The answer is B
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A circular tabletop is to be cut from a square piece of wood [#permalink] New post   20 Apr 2022, 11:58
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Well

My explanation versus yours is kinda like a city car versus a Lamborghini :lol: :lol: :lol:
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A circular tabletop is to be cut from a square piece of wood [#permalink] New post   20 Apr 2022, 12:05
Carcass wrote:
Well

My explanation versus yours is kinda like a city car versus a Lamborghini :lol: :lol: :lol:


Thanks for the kind words, Carcass!!
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Re: A circular tabletop is to be cut from a square piece of wood [#permalink] New post   12 Jul 2022, 20:35
Assume: r = 7
area of the circle = 22/7 * 7 * 7 = 154
area of the square = 14 x 14 = 196
unused area = 196 - 154 = 42
unused area (%) = 42/196 = 21.4..%
21.4…% < 25%
Correct answer: B. The quantity in Column B is greater.
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Re: A circular tabletop is to be cut from a square piece of wood [#permalink] New post   13 Jul 2022, 06:38
B)The quantity in Column B is greater.
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Re: A circular tabletop is to be cut from a square piece of wood [#permalink]
13 Jul 2022, 06:38
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