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ratio problem

Expert replies
by princessss » Sun Oct 10, 2010 2:00 am
When a tree was planted it was 4 feet. Its height increased by a constant amount each year for 6 years. after 6 years the tree was 1/5 taller than at the end of 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
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Source: — Problem Solving |

by goyalsau » Sun Oct 10, 2010 2:46 am
princessss wrote:When a tree was planted it was 4 feet. Its height increased by a constant amount each year for 6 years. after 6 years the tree was 1/5 taller than at the end of 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
What i am getting as answer is (6/5)^1/2
Or to say sq rt of 6/5

what is the OA ?
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by princessss » Sun Oct 10, 2010 3:18 am
correct is 2/3.

I can't get it I always get 2/5 :-/
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by selango » Sun Oct 10, 2010 3:23 am
Tree height increases by constant k every year.

At the end of 4thyear=4+4k

At the end of 6thyear=4+6k

Height of 6th year is 1/5 or 20% more than height of 4th year.

4+6k=4+4k+1/5(4+4k)

k=2/3
--Anand--
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by GMATGuruNY » Sun Oct 10, 2010 3:24 am
princessss wrote:When a tree was planted it was 4 feet. Its height increased by a constant amount each year for 6 years. after 6 years the tree was 1/5 taller than at the end of 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
We can plug in the answers, which represent the increase in height each year. We need to determine the height after 4 years and the height after 6 years. Increasing the height after 4 years by 1/5 must yield the height after 6 years. Let h = height.

Answer choice C:
After 4 years, h = 4 + 4*(1/2) = 6.
After 6 years, h = 6 + 2(1/2) = 7.
Doea 6 + (1/5)*6 = 7? No.

Answer choice D:
After 4 years, h = 4 + 4*(2/3) = 20/3.
After 6 years, h = 20/3 + 2(2/3) = 24/3.
Does 20/3 + (1/5)*20/3 = 24/3? Yes!

The correct answer is D.
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