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PS Problem from GMATPrep

This topic has 1 expert reply and 3 member replies
Tsadori Newbie | Next Rank: 10 Posts Default Avatar
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Posted:
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PS Problem from GMATPrep

Post Sun Jan 21, 2007 2:15 pm
SOURCE: GMATPrep
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GMAT/MBA Expert

Post Fri Oct 06, 2017 6:24 pm
Quote:
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)πr²
B)πr² + 10
C)π)r² + 1/4(π² * r²)
D)πr² + (40 - 2[pi] * r)²
E)πr² + (10 - 1/2[πr)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) π(0²) = 0 NOPE
B) π(0²) + 10 = 10 NOPE
C) π(0²) + 1/4(π² * 0²) = 0 NOPE
D) π(0²) + (40 - 2π0)² = 1600 NOPE
E) π(0²) + (10 - 1/2[π](0))² = 100 PERFECT!

Answer: E

Cheers,
Brent

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Post Fri Oct 06, 2017 6:09 pm
let say the piece of wire was divided into two equally,
(1) circumference of the circle is 2πr = 20
r = 10/π, area = πr^2 = π (10/π)^2
area of circle = 100 / π

(2) Perimeter of square = 4 * side = 20
side = 20/4 = 5, area = 5^2 = 25
the total area is 100/π + 25
Now, let us substitute the value of r= 10/ π in the answer choices and see which one gives 100/π + 25

In option A, πr^2 = π (10/π)^2 = 100/π wrong
in option B, πr^2 + 10 = 100/π +10 wrong
in option C, πr^2 + (1/4) π^2 r^2 = (100/π) + 1/4 * π^2 * (10/π)^2
= 100/π + 25 correct
in option D, πr^2 + (40 - 2πr)^2 = 100/π [40 - 2π (10/π)]^2
=100/π + (40-20)^2
100/π + 400 wrong
in option E, πr^2 + (10 - 1/2 * πr^2) = 100/π + [10- 1/2π (10/π)^2]
=100/π + (10-5)^2
100/π + 25 correct

option C and E seem to be the two correct answer to this question

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g2000 Junior | Next Rank: 30 Posts Default Avatar
Joined
09 Jan 2007
Posted:
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Post Sun Jan 21, 2007 3:44 pm
40 = Circumference of square + perimeter of square

We are to find the sum of areas of both.
Area of circle = pi * r^2
Area of Square = m^2 where m is the one side length of square

4*m = 40 - (2 * pi * r)
m = ( 40 - (2 * pi * r) ) / 4
m = (10 - ((pi * r ) / 2 ) )

Total area enclosed by both shapes
= area of circle + area of square
= (pi * r ^ 2) + (10 - (( pi * r)/ 2)) ^ 2

Answer is the last choice

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Tsadori Newbie | Next Rank: 10 Posts Default Avatar
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Posted:
4 messages
Post Mon Jan 22, 2007 2:15 pm
OA: E

Thanks Smile

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