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 6th year, the tree was 1/5 taller than it was at the end of 4th year. By how many feet the height of the tree increase each year?
A) 3/10
B) 2/5
C) 1/2
D) 2/3
E) 6/5
And then there's always good old-fashioned back-solving. Say we test C, 1/2, or .5
End Year 1: 4 + 1/2 = 4.5
End Year 2: 4.5 + 1/2 = 5
End Year 3: 5 + 1/2 = 5.5
End Year 4: 5.5 + 1/2 = 6
End Year 5: 6 + 1/2 = 6.5
End Year 6: 6.5 + 1/2 = 7
Here between year 4 and year 6, we have an increase of 7 - 6 or 1. If the height at the end of year 4 was 6, the percent increase would be (1/6) * `100 = 16.67%. (Even without calculating, clearly 1/6 is less than 20% as 1/5 = 20%.) So 1/2 is too small. Eliminate A, B, and C.
Now you just have to test either D or E. If the one you test works, you have your answer. If the one you test doesn't work, the other one must be correct.
(Note that you can pretty much reason that D will have to be correct. 16.67% is pretty close to 20%. So if 1/2 is very close to the value we're looking for, it would't make much sense for 6/5 to be our answer, as 6/5 is more than double 1/2.)
Test D
End Year 1: 4 + 2/3
End Year 2: 4 + 4/3
End Year 3: 4 + 6/3
End Year 4: 4 + 8/3
End Year 5: 4 + 10/3
End Year 6: 4 + 12/3
End Year 4: 4 + 8/3 = 12/3 + 8/3 = 20/3
End Year 6: 4 + 12/3 = 4 + 4 = 8 = 24/3
Difference: 24/3 - 20/3 = 4/3
Percent Change [(4/3)/(20/3)] * 100 = 20%.
D is correct.
