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height of tree

This topic has 3 expert replies and 2 member replies
josh80 Senior | Next Rank: 100 Posts Default Avatar
Joined
03 Nov 2013
Posted:
72 messages
Thanked:
1 times

height of tree

Post Wed Dec 11, 2013 5:20 pm
Elapsed Time: 00:00
  • 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 Junior | Next Rank: 30 Posts
    Joined
    08 Aug 2016
    Posted:
    13 messages
    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 Junior | Next Rank: 30 Posts
    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

    Check out the online reviews of our course
    Come see all of our free resources

    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!
    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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