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 1250 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. Choose the correct choice from the following answers
A) 513  B) 512  C) 517  D) 519  E) 521
Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, C, D,E The answer to be B   Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year.   If x = initial number of trees = 512   Year 1 = 5/4x   Year 2 = (5/4)(5/4)x   Year 3 = (5/4)(5/4)(5/4)x   Year 4 = (5/4)(5/4)(5/4)(5/4)x   Only for Answer D: (5/4)(5/4)(5/4)(5/4) 512 = 1250   Hence, correct answer = 512
<result>B</result>
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 1250 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.