During a two week period, the price of an ounce o silverincreased by 25 percent by the end of the first week an then decreased by 20 percent of this new price by the end of the second week. If the price of the silver was x dollars per ounce by the beginning of the two-week period, what was the price, in dollars per ounce, by the end of the period?
A 0.8x
B 0.95x
C x
D 1.05x
E 1.25x
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This variation calculations are frquent in GMAT. We have already proposed some examples of these. An alternative approach to the one proposed will now be given (see PS (problem solving) copper price http://gmatportugal.blogspot.com/2006/02/ps-problem-solving-copper-price.html).
if the variations are multiple of "friendly" percentages such as 10%, 20%, 25%, we can look for a fraccional equivalent of the variations result. So an increase of 10%, 20% or 25%, would represent a multiplication of the original value by 11/10, 6/5 or 5/4 respectively. Why? That's what we get from adding 1 (the original value) to a increase of 1/10 (10%), 1/5 (20%) or 1/4 (25%).
When the variation is negative, when the price (or whatever other quantity) is decreased by 10%, 20% or 25%, we subtract from "our" unity 1/10 (for 10%), 1/5 (for 20%) or 1/4 (for 25%), resulting in a multiplying factor of 9/10 (-10%), 4/5 (-20%) or 3/4 (-25%).
In our case we will multiply the factors corresponding to an increase of 25% and then a decrease of 20%. That means that the factor from the initial to the final value will be (5/4)x(4/5) which is obviously 1. So if x is the original price, 1.x will certainly be the final price, and the correct answer is (C)
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