As discussed, let's look at one of the innovative ways of solving the above question.
It is one of the quickest ways to solve a question that involves successive percentage increase/decrease on the same value. Please take a note of this approach and apply it on some GMAT questions to master it.
So, let's quickly look at this
smart approach. When a number is
increased successively by two percentage, let's assume, \(a\)% and \(b\)%, the net increase in the value of the number can be expressed by the formula,
Net increase \(=a+b+\frac {ab}{100}\)
Le's take a simple example to understand. If we increase a number, let's say, X successively by 10% and 20% respectively, the net increase according to the above formula should be,
Net increase \(=10+20+\frac {10*20}{100}=10+20+\frac {200}{100} = 10+20+2 = 32\)%
Isn't that quick!! A nice method to keep in your arsenal to solve Percent question involving successive increase quickly. One good thing about the above formula is that you can use it to calculate the net decrease in case of successive decrease too.
All you need to do is in case of decrease represent the percent as negative. Easy isn't it . Let's see an application quickly.
If we decrease a number, let's say, X successively by 10% and 20% respectively, the net increase according to the above formula should be,
Net increase \(=(-10)+(-20)+\frac {(-10)*(-20)}{100}=-10-20+\frac {200}{100} = -10-20+2 = (-28)\)%
Notice carefully, the sign of the net increase is negative, clearly indicating the after the successive decrease the value of the original number, decreased instead of increasing. And what was the magnitude??? Right 28%. The net decrease is 28%.
So, before we use this approach to give you an official answer for the above question, would you like to have a quick stab at it. Remember, you need to be careful about the sign of the change. Increase is represented by positive and decrease is represented by negative. All the best.
We will post the detailed solution tomorrow and then we will show another innovative method of solving this question.
Regards,
Saquib
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