Linear Sequence Problem

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szDave: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sat Oct 27, 2012 11:12 amFollowed by: 1 member

by szDave » Mon Jan 21, 2013 4:01 am

Hello,

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 1/5 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

This exercise seems so easy, but I don't find the solution. Mine was 1/10 (2years increase = 1/5, so 1 year increase is 1/10, but it's not correct)

Please help me with this

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Source: Beat The GMAT — Problem Solving | Mon Jan 21, 2013 4:01 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jan 21, 2013 4:39 am

szDave wrote:Hello,

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 1/5 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

This exercise seems so easy, but I don't find the solution. Mine was 1/10 (2years increase = 1/5, so 1 year increase is 1/10, but it's not correct)

Please help me with this

Let the height by which the tree increased constantly each year be x ft.
At the end of the 1st year, height of tree = 4 + x
At the end of the 2nd year, height of tree = 4 + 2x
...
At the end of the 6th year, height of the tree = 4 + 6x
It is 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, so 4 + 6x = (1 + 1/5) * (4 + 4x)
Solving, we get, 20 + 30x = 24 + 24x
6x = 4
x = [spoiler]2/3[/spoiler]

The correct answer is D.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jan 21, 2013 5:05 am

When a 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 6th year ,the tree was 1/5 taller than it was end of the 4th year .By how many feet did the height of tree increase each year

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

An alternate approach is to plug in the answer choices, which represent the yearly height increase.

Answer choice C: 1/2
Height after 4 years = 4 + 4(1/2) = 6.
Height after 6 years = 6 + 2(1/2) = 7.
(difference between the two heights)/(height after 4 years) = (7-6)/6 = 1/6.
Since the height must increase by 1/5 -- a value GREATER than 1/6 -- a greater answer choice is needed.

Answer choice D: 2/3
Height after 4 years = 4 + 4(2/3) = 20/3.
Height after 6 years = 20/3 + 2(2/3) = 24/3.
Since the two fractions have the same denominator, we can use the numerators to determine by what fraction the height here has increased:
(difference between the two heights)/(height after 4 years) = (24-20)/20 = 4/20 = 1/5.
Success!

The correct answer is D.

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rupeshrch: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Jan 22, 2013 4:45 pm

by rupeshrch » Thu Jan 24, 2013 2:49 pm

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Triangle: (X+Y)/6 = Y/2

So, X = 2Y

Also Y = (4+X)/5

So, Y = 4/3 and X = 8/3.

Yearly rate, (X+Y)/6 = 12/3*6 = 2/3

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