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arithmetic problem

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arithmetic problem

by rerika01 » Mon Jul 04, 2011 7:06 pm
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

How to arrive to the correct answer d)?

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by Frankenstein » Mon Jul 04, 2011 7:13 pm
Hi,
Let the tree increase by an amount x every year.
So, at the end of 4th year, height is 4+4x
and at the end of 4th year, height is 4+6x
Given that (4+6x) = (6/5)(4+4x)
So, 20+30x = 24+24x
So, x=2/3

Hence, D
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by amit2k9 » Mon Jul 04, 2011 8:55 pm
let the increase/year be = k.

thus, 1st year height = 4+k 2nd year height = 4+2k....6th year height = 4+6k

now, 4+6k- (4+4k) = 1/5(4+4k)

thus k= 4/6=2/3
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