Please explain,which approach will better, whether to use algebra or to plugin numbers??
A thin piece of wire 40 metres long...
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Given that the circle has a radius of r units, its circumference must be 2(pi)r. And the remaining wire makes up the perimeter of the square, i.e. 40  2(pi)r. Since a square consists of four equal sides, we can determine the length of a side by dividing the perimeter by 4. Thus, each side is 10  (pi)r/2. And the area of the square is given by (10  (pi)r/2)^2. The area of the circle is (pi)r^2. And the total area is (pi)r^2 + (10  (pi)r/2)^2, which is answer choice E.
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Would definitely rely on an algebraic approach. You would need to do a lot of math if you chose numbers. Because you'd have to compare your result with each answer choice. The algebra is not too terrible on this one. I know sometimes it gets pretty bad, especially with compounding interest and things of that sort.
800 or bust!
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 Brent@GMATPrepNow
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One approach is to plug in a value for r and see what the output should be.A thin piece of 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in term of r?
A)(pi)rÂ²
B)(pi)rÂ² + 10
C)(pi)rÂ² + 1/4([pi]Â² * rÂ²)
D)(pi)rÂ² + (40  2[pi] * r)Â²
E)(pi)rÂ² + (10  1/2[pi] * r)Â²
Let's say r = 0. That is, the radius of the circle = 0
This means, we use the entire 40meter length of wire to create the square.
So, the 4 sides of this square will have length 10, which means the area = 100
So, when r = 0, the total area = 100
We'll now plug r = 0 into the 5 answer choices and see which one yields an output of 100
A) (pi)(0Â²) = 0 NOPE
B) (pi)(0Â²) + 10 = 10 NOPE
C) (pi)(0Â²) + 1/4([pi]Â² * 0Â²) = 0 NOPE
D) (pi)(0Â²) + (40  2[pi]0)Â² = 1600 NOPE
E) (pi)(0Â²) + (10  1/2[pi](0))Â² = 100 PERFECT!
Answer: E
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Brent
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 Brent@GMATPrepNow
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Here's an algebraic approach:A thin piece of 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in term of r?
A)(pi)rÂ²
B)(pi)rÂ² + 10
C)(pi)rÂ² + 1/4([pi]Â² * rÂ²)
D)(pi)rÂ² + (40  2[pi] * r)Â²
E)(pi)rÂ² + (10  1/2[pi] * r)Â²
Since r is the radius of the circle, the area of the circle will be (pi)rÂ²
If r is the radius of the circle, the length of wire used for this circle will equal its circumference which is 2(pi)r
So, the length of wire to be used for the square must equal 40  2(pi)r
In other words, the perimeter of the square will be 40  2(pi)r
Since squares have 4 equal sides, the length of each side of the square will be [40  2(pi)r]/4, which simplifies to be 10  (pi)r/2
If each side of the square has length 10  (pi)r/2, the area of the square will be [10  (pi)r/2]Â²
So, the total area will equal (pi)rÂ² + [10  (pi)r/2]Â², which is the same as E
Cheers,
Brent
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 Brent@GMATPrepNow
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We demonstrated the two methods (Algebraic and InputOutput) for solving a question type I call Variables in the Answer Choices.
If you'd like more information on these approaches, we have some videos:
 Variables in the Answer Choices  https://www.gmatprepnow.com/module/gmat ... /video/933
 Tips for the Algebraic Approach  https://www.gmatprepnow.com/module/gmat ... /video/934
 Tips for the InputOutput Approach  https://www.gmatprepnow.com/module/gmat ... /video/935
Here are some more questions to practice with:
 https://www.beatthegmat.com/whatmistake ... 76293.html
 https://www.beatthegmat.com/cardealers ... 74136.html
 https://www.beatthegmat.com/psratetimest276107.html
 https://www.beatthegmat.com/tofindthe ... 73338.html
 https://www.beatthegmat.com/ydollarsfr ... 73031.html
 https://www.beatthegmat.com/metersinx ... 73854.html
 https://www.beatthegmat.com/abetterexp ... 79396.html
Cheers,
Brent
If you'd like more information on these approaches, we have some videos:
 Variables in the Answer Choices  https://www.gmatprepnow.com/module/gmat ... /video/933
 Tips for the Algebraic Approach  https://www.gmatprepnow.com/module/gmat ... /video/934
 Tips for the InputOutput Approach  https://www.gmatprepnow.com/module/gmat ... /video/935
Here are some more questions to practice with:
 https://www.beatthegmat.com/whatmistake ... 76293.html
 https://www.beatthegmat.com/cardealers ... 74136.html
 https://www.beatthegmat.com/psratetimest276107.html
 https://www.beatthegmat.com/tofindthe ... 73338.html
 https://www.beatthegmat.com/ydollarsfr ... 73031.html
 https://www.beatthegmat.com/metersinx ... 73854.html
 https://www.beatthegmat.com/abetterexp ... 79396.html
Cheers,
Brent
Brent Hanneson  Creator of GMATPrepNow.com
If you enjoy my solutions, you'll love my GMAT prep course!
Watch these video reviews of my course
And check out these free resources
If you enjoy my solutions, you'll love my GMAT prep course!
Watch these video reviews of my course
And check out these free resources