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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
Joined
16 Nov 2006
Posted:
4 messages

PS Problem from GMATPrep

Post Sun Jan 21, 2007 2:15 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
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    g2000 Junior | Next Rank: 30 Posts Default Avatar
    Joined
    09 Jan 2007
    Posted:
    19 messages
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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

    Tsadori Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    16 Nov 2006
    Posted:
    4 messages
    Post Mon Jan 22, 2007 2:15 pm
    OA: E

    Thanks Smile

    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

    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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