height of tree

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josh80 Rising GMAT Star Default Avatar
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height of tree Post Wed Dec 11, 2013 5:20 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

    - 3/10
    - 2/5
    - 1/2
    - 2/3
    - 6/5

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    Post Wed Dec 11, 2013 5:25 pm
    Quote:
    When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a certain amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

    A. 3/10
    B. 2/5
    C. 1/2
    D. 2/3
    E. 6/5
    Height of tree on day 0 = 4
    Let d = the height increase each year
    Height of tree at the end of the 1st year = 4+d
    Height of tree at the end of the 2nd year = 4+d+d = 4 + 2d
    Height of tree at the end of the 3rd year = 4+d+d+d = 4 + 3d
    Height of tree at the end of the 4th year = 4+d+d+d+d = 4 + 4d
    Height of tree at the end of the 5th year = 4+d+d+d+d+d = 4 + 5d
    Height of tree at the end of the 6th year = 4+d+d+d+d+d+d = 4 + 6d

    At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year
    In other words, 6th year height = 4th year height + 1/5(4th year height)
    Or we can write 4 + 6d = (4 + 4d) + 1/5(4 + 4d)
    Simplify: 4 + 6d = 6/5(4 + 4d)
    Multiply both sides by 5 to get: 5(4 + 6d) = 6(4 + 4d)
    Expand: 20 + 30d = 24 + 24d
    Simplify: 6d = 4
    d = 4/6 = 2/3 = D

    Cheers,
    Brent

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    Thanked by: josh80
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    jervizeloy Just gettin' started!
    Joined
    08 Aug 2016
    Posted:
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    Post Wed Aug 24, 2016 1:57 pm
    Brent@GMATPrepNow wrote:
    Quote:
    When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a certain amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

    A. 3/10
    B. 2/5
    C. 1/2
    D. 2/3
    E. 6/5
    Height of tree on day 0 = 4
    Let d = the height increase each year
    Height of tree at the end of the 1st year = 4+d
    Height of tree at the end of the 2nd year = 4+d+d = 4 + 2d
    Height of tree at the end of the 3rd year = 4+d+d+d = 4 + 3d
    Height of tree at the end of the 4th year = 4+d+d+d+d = 4 + 4d
    Height of tree at the end of the 5th year = 4+d+d+d+d+d = 4 + 5d
    Height of tree at the end of the 6th year = 4+d+d+d+d+d+d = 4 + 6d

    At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year
    In other words, 6th year height = 4th year height + 1/5(4th year height)
    Or we can write 4 + 6d = (4 + 4d) + 1/5(4 + 4d)
    Simplify: 4 + 6d = 6/5(4 + 4d)
    Multiply both sides by 5 to get: 5(4 + 6d) = 6(4 + 4d)
    Expand: 20 + 30d = 24 + 24d
    Simplify: 6d = 4
    d = 4/6 = 2/3 = D

    Cheers,
    Brent
    Hi Brent, please help me out with something...I've thought about solving this problem following the scheme detailed below:

    Year 1: 4
    Year 2: 4R2
    .
    .
    .
    .
    Year 6: 5R5

    What's the flaw of my thinking? Thanks in advance

    jervizeloy Just gettin' started!
    Joined
    08 Aug 2016
    Posted:
    13 messages
    Post Wed Aug 24, 2016 1:58 pm
    Brent@GMATPrepNow wrote:
    Quote:
    When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a certain amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

    A. 3/10
    B. 2/5
    C. 1/2
    D. 2/3
    E. 6/5
    Height of tree on day 0 = 4
    Let d = the height increase each year
    Height of tree at the end of the 1st year = 4+d
    Height of tree at the end of the 2nd year = 4+d+d = 4 + 2d
    Height of tree at the end of the 3rd year = 4+d+d+d = 4 + 3d
    Height of tree at the end of the 4th year = 4+d+d+d+d = 4 + 4d
    Height of tree at the end of the 5th year = 4+d+d+d+d+d = 4 + 5d
    Height of tree at the end of the 6th year = 4+d+d+d+d+d+d = 4 + 6d

    At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year
    In other words, 6th year height = 4th year height + 1/5(4th year height)
    Or we can write 4 + 6d = (4 + 4d) + 1/5(4 + 4d)
    Simplify: 4 + 6d = 6/5(4 + 4d)
    Multiply both sides by 5 to get: 5(4 + 6d) = 6(4 + 4d)
    Expand: 20 + 30d = 24 + 24d
    Simplify: 6d = 4
    d = 4/6 = 2/3 = D

    Cheers,
    Brent
    Hi Brent, please help me out with something...I've thought about solving this problem following the scheme detailed below:

    Year 1: 4
    Year 2: 4R2
    .
    .
    .
    .
    Year 6: 5R5

    What's the flaw of my approach? Thanks in advance

    Post Wed Aug 24, 2016 2:40 pm
    jervizeloy wrote:
    Hi Brent, please help me out with something...I've thought about solving this problem following the scheme detailed below:

    Year 1: 4
    Year 2: 4R2
    .
    .
    .
    .
    Year 6: 5R5

    What's the flaw of my approach? Thanks in advance
    Hi jervizeloy,

    Sorry, but I'm not sure what 4R2 and 5R5 mean. Can you elaborate on this?

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Enter our contest to win a free course.

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

    GMAT/MBA Expert

    Post Thu Aug 25, 2016 4:07 pm
    josh80 wrote:
    When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

    - 3/10
    - 2/5
    - 1/2
    - 2/3
    - 6/5
    When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. Since we know that the growth is by a constant amount we have a linear growth problem. Thus we can label the growth by year where x = the yearly growth amount, in feet:

    Starting height = 4

    height after year one = 4 + x

    height after year two = 4 + 2x

    height after year three = 4 + 3x

    height after year four = 4 + 4x

    height after year five = 4 + 5x

    height after year six = 4 + 6x

    We are also given that at the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. This means the height of the tree at the end of the 6th year is 6/5 times as tall as its height at the end of the 4th year. Thus we can create the following equation:

    (6/5)(4 + 4x) = 4 + 6x

    To eliminate the fraction of 6/5 we can multiply the entire equation by 5.

    6(4 + 4x) = 20 + 30x

    24 + 24x = 20 + 30x

    6x = 4

    x = 4/6 = 2/3 feet

    Answer: D

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