imhimanshu 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
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Useful to know your Powers of 4 \(5^4 = 625\) and \(4^4 = 256\)
"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"
This translate into:
\(Year 1 = X *\) \(\frac{5}{4}\)
\(Year 2 = X *\) \(\frac{5}{4}\) * \(\frac{5}{4}\)
\(Year 3 = X *\) \(\frac{5}{4}\) * \(\frac{5}{4}\) * \(\frac{5}{4}\)
\(Year 4\) or 6250 trees \(= X *\) \(\frac{5}{4}\) * \(\frac{5}{4}\) * \(\frac{5}{4}\) * \(\frac{5}{4}\)
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\(6250 = X *\) \(\frac{5^4}{4^4}\)
\(625 * 10 = X *\) \(\frac{5^4}{4^4}\)
\(25^2 * 10 = X *\) \(\frac{5^4}{4^4}\)
\(5^4 * 10 = X *\) \(\frac{5^4}{4^4}\)
(The \(5^4\) cancel out, leaving \(4^4\))\(4^4 * 10 = X\)
\(256 * 10 = X\)
\(2560 = X\)
Answer is D