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
Can someone walk me through the logic behind this question. I am able to solve this by using options as well as by assuming the number of trees = x. However, had the question been, "If all of the trees thrived and there were 6250 trees in the orchard at the end of 15 year period, how many trees were in the orchard at the beginning of the 4 year period". then it would have been difficult to solve.
Thanks
The number of trees increases by 1/4 i.e. 25% every year. It is just a matter of thinking in terms of successive percentage changes e.g. population increase. Here, we are talking about the increase of tree population.
If x increases by 25%, how we denote it? (5/4)*x
If next year, this new number increases by 25% again, how do we denote it? (5/4)*(5/4)*x
and so on...
For more on this, check:
http://www.veritasprep.com/blog/2011/02 ... e-changes/So if we are taking into account 4 years, we simply get (5/4)^4 * x = 6250
As for your next question, the numbers given would be such that the calculation will not be tough.
Say, you have 8 years and 100% increase every year (population doubles every year). The final population will be divisible by 2^8 i.e. 256.
Something like 2^8 * x = 2560
and if you meant what you wrote (though I considered that the 4 was a typo because of the language of the question) "If all of the trees thrived and there were 6250 trees in the orchard at the end of
15 year period, how many trees were in the orchard at the beginning of
the 4 year period", note that you still need to work with
(5/4)^4 * x = 6250
since you need the number of trees 4 yrs back only. The only thing is that the answer (2560) needs to be divisible by \(5^{11}\) which it isn't so there is a problem in this question. If it were an actual question, the answer would be divisible by \(5^{11}\) but you wouldn't really need to bother about it.
Thanks! But how do you know when to solve difficult fractions, rather than to use a shortcut? I guessed on the question because I figured I had missed a strategy to avoid solving (1.25)^4 or (5/4)^4