From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 20 percent. What percent of the stock’s 2007 starting price was the price of the stock at the end of 2009? A. 80 B. 90 C. 95 D. 100 E. 108
(E) This problem is most easily solved by picking a number for the price at the beginning of 2007, and then determining what the prices would be in 2008 and 2009, given that starting number.
Since we are dealing with percents, let’s start with $100 for the price at the beginning of 2007. By the end of 2007, the price had risen 20 percent, up to $120. In 2008, the price dropped 25 percent, but it dropped from $120, not from the original $100. So the price at the end of 2008 was: $120 – 0.25 × ($120) = $120 – $30 = $90.
In 2009, the stock price rose by 20 percent, but it rose from $90, not from $100 or $120. So the price at the end of 2009 was: $90 + 0.20 × ($90) = $90 + $18 = $108.
Now, since our starting value was $100, the question is really asking was percent $108 is of $100: $108 is 108% of $100.
The correct answer is choice (E). -------------
You can also use logic to solve this, just thinking about it, x is up by 20% then down 25% then up 20% is greater than x and since the only number greater than x is answer e (108) this should be so.
I would not advise using rough approximation in percentages questions. If you do so you must be totally sure there is some margin in your approximations, because sometimes numbers can get very tricky.
The reason for is that every time we have a different value as 100%, when we deduct or add percentage increase/decrease. For example, if x rose by 50% then decreased by 70% and then rose by 50% again in the result we get 32,5% decrease though it might seem that increase (50% in the beginning and 50% afterwards) was bigger.
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