Each year for 4 years, a farmer increased the number of

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Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752

OA D.

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Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period?

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752
Here's another approach:

First notice that, if the number of trees increases by 1/4, then the new number is 5/4 times the original number.

Let x = the # of trees in the orchard at the beginning of the 4 year period.
(5/4)x = # of trees after 1 year
(5/4)(5/4)x = # of trees after 2 years
(5/4)(5/4)(5/4)x = # of trees after 3 years
(5/4)(5/4)(5/4)(5/4)x = # of trees after 4 years

We're told that, after 4 years, there are 6250 trees, so we now know that:
(5/4)(5/4)(5/4)(5/4)x = 6250
(625/256)x = 6250
x = 6250(256/625)
x = 2560

Answer: D

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by GMATGuruNY » Fri Oct 05, 2018 12:11 pm
AAPL wrote:Official Guide

Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752
We can PLUG IN THE ANSWERS, which represent the original number of trees.
Since the number of trees increases by 1/4 each year, the correct answer must be a multiple of 4.
The last 2 digits of a multiple of 4 must themselves form a multiple of 4.
Eliminate A (1250) and C (2250), since 50 is not a multiple of 4.
Eliminate B (1563), since 63 is not a multiple of 4.

Answer choice D: 2560
After the 1st year, the number of trees = 2560 + (1/4)2560 = 3200.
After the 2nd year, the number of trees = 3200 + (1/4)3200 = 4000.
After the 3rd year, the number of trees = 4000 + (1/4)4000 = 5000.
After the 4th year, the number of trees = 5000 + (1/4)5000 = 6250.
Success!

The correct answer is D.

Note that we had to test only ONE answer choice -- a very efficient way to solve the problem.
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by Scott@TargetTestPrep » Thu Oct 18, 2018 5:32 pm
AAPL wrote:Official Guide

Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752
This problem is testing us on exponential growth. We are given that the number of trees increased by ¼ each year. To determine the number of trees in a certain year, we multiply the number of trees from the previous year by 1.25, or 5/4. Let's let x equal the number of trees at the beginning (of the first year) of the 4-year period.

Start of year 1 = x

End of year 1 = x(5/4)

End of year 2 = x(5/4)(5/4)

End of year 3 = x(5/4)(5/4)(5/4)

End of year 4 = x(5/4)(5/4)(5/4)(5/4) = (625/256)x

We are given that there were 6,250 trees at the end of year 4, so we can set up the following equation:

(625/256)x = 6,250

625x = 6,250(256)

x = 10(256) = 2,560

Thus, there were 2,560 trees at the beginning of the 4-year period.

Answer: D

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