B166418 wrote: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.