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didn't know how to answer this problem from the GMAT PREP!!

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by Brent@GMATPrepNow » Mon Nov 18, 2013 4:48 pm
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)r²
B)(pi)r² + 10
C)(pi)r² + 1/4([pi]² * r²)
D)(pi)r² + (40 - 2[pi] * r)²
E)(pi)r² + (10 - 1/2[pi] * r)²
One approach is to plug in a value for r and see what the output should be.

Let's say r = 0. That is, the radius of the circle = 0
This means, we use the entire 40-meter 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)(0²) = 0 NOPE
B) (pi)(0²) + 10 = 10 NOPE
C) (pi)(0²) + 1/4([pi]² * 0²) = 0 NOPE
D) (pi)(0²) + (40 - 2[pi]0)² = 1600 NOPE
E) (pi)(0²) + (10 - 1/2[pi](0))² = 100 PERFECT!

Answer: E

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Mon Nov 18, 2013 4:52 pm, edited 1 time in total.
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by aalradadi » Mon Nov 18, 2013 4:52 pm
man your the best!!! even the companies that charged me money did not replay this fast!! thanks Brent!

any advise for someone will take the test this Thursday?

I took it 8 weeks ago and I scored 580
am aiming for 630

my last to cat were 600 and 630 from Kaplan.
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by Brent@GMATPrepNow » Mon Nov 18, 2013 4:54 pm
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)r²
B)(pi)r² + 10
C)(pi)r² + 1/4([pi]² * r²)
D)(pi)r² + (40 - 2[pi] * r)²
E)(pi)r² + (10 - 1/2[pi] * r)²
Here's another approach:

Since r is the radius of the circle, the area of the circle will be (pi)r²

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]²

So, the total area will equal (pi)r² + [10 - (pi)r/2]², which is the same as E

Cheers,
Brent
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by Brent@GMATPrepNow » Mon Nov 18, 2013 4:56 pm
aalradadi wrote:man your the best!!! even the companies that charged me money did not replay this fast!! thanks Brent!

any advise for someone will take the test this Thursday?

I took it 8 weeks ago and I scored 580
am aiming for 630

my last to cat were 600 and 630 from Kaplan.
Thanks aalradadi,

With 3 days left to prepare, I suggest you take another practice test or two to work on your test-taking skills (time management, endurance, etc)

Cheers,
Brent
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by theCodeToGMAT » Mon Nov 18, 2013 8:57 pm
Let one length be "x" other be 40-x

2 * pi * r = x

4 * side = 40-x

To find: Area of Circle + Area of Square

pi * (r)^2 + Side^2

pi*r^2 + [(40 - x)/4]^2

pi*r^2 + [(40 - 2*pi*r)/4]^2

pi*r^2 + [(10 - pi*r/2)]^2

Answer [spoiler]{E}[/spoiler]
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by sanju09 » Mon Nov 18, 2013 11:01 pm
aalradadi wrote:How can I answer this problem?

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Let's plug in r = 2. If π is approximately equal to 3, then this would require 12 meters of wire to form the circle whose area will also be approximately equal to 12. We'll be left with approximately 28 meters of wire to form the square whose area will be approximately equal to 49. Thus the combined area would be approximately equal to 61. So when r = 2, our target answer is 61. Let's now check the answers...

A. πr^2 means 12, cross it off!
B. πr^2 + 10 means 22, cross it off!
C. πr^2 + ¼ π^2r^2 means 21, cross it off!
D. πr^2 + (40 - 2πr)^2 means 12 + 28^2, too big, cross it off!
E. Enjoy!
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