Problem Solving

[email protected] wrote: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

Algebraic Approach:
The number of trees in a year is increased by 1/4 of the number of trees in the preceding year. Hence, number of trees in a year = (1 + 1/4) = 5/4 of the number of trees in the preceding year.

Let us assume that number of trees at the beginning of the year = N
So, N*(5/4)*(5/4)*(5/4)*(5/4) = 6250
--> N = 6250*(4/5)*(4/5)*(4/5)*(4/5) = 6250*(4^4)/(5^4) = 6250*256/625 = 2560

The correct answer is D.

This particular problem can be solved easily by efficiently plugging the answer choices also.

Note that in the 2nd year the number of trees increased by 1/4 of the of the number of of trees in the 1st year. Hence, number of trees in the first year, i.e. the correct answer must be a multiple of 4.

So, the last two digits of the correct answer must be multiple of 4.
Discard A, B, and C.

Check with option D : 2560
2560*(5/4)*(5/4)*(5/4)*(5/4) = 2560*(5^4)/(4^4) = 2560*625/256 = 6250 --> Correct

The correct answer is D.