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gmatprep word problem

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gmatprep word problem

by maolivie » Thu Jul 05, 2007 6:32 pm
When a certain tree was first planted, it was four feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. By the end of the 6th year the height of the tree was 1/5 taller than it was by the end of the 4th year.By how many feet did the height of the tree increase each year?

1-3/10
2-2/5
3-1/2
4-2/3
5-6/5

I get 2/5, OA is 2/3. What the __ is going on here?
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by thumpin_termis » Thu Jul 05, 2007 6:42 pm
Here's how I set it up.

let x be the growth in each year
so at the end of 4th year, the tree is 4+4x tall, and at the end of 6th year, it's 4+6x.

Is states that at the end of 6th year, the tree is 1/5 taller, which means it's 20% taller, or that it's 6/5 height of the tree from its 4th year. Algebraically, we set that up as

4+6x = (6/5)(4+4x)
4+6x = (24+24x) / 5
24 + 24x = 5(4+6x) : cross multiplied
24 + 24x = 20 + 30x
6x = 4
x = 2/3
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