# Fast way to manually calculate percentage increments/decrements

I'm currently studying for the GMAT exam, and I'd like to know if there's a way to manually (and quickly) determine an increment/decrement percent between two numbers.

I know for example, that if I take 5 as my $100%$ reference value and I then compare it against $15$, I find that there was a $200%$ increment with the following formula:

$\text{dPctg}=\frac{15\times100}{5}-100$

However, is there a faster way to get to this fact? Or at least achieve it with less calculations?

Please let me know if there's anything else I may be missing.

Thank you for your time and help!

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If 5 is 100%, then $15=3\times 5$ is $3\times100\%$.Your increase is then $300-200=$... –  Guess who it is. Oct 31 '11 at 21:10

Perhaps $\left(\frac{\textrm{new value}}{\textrm{reference value}} - 1\right) \times 100$ is what you need.

Example: $\left(\frac{15}{5}-1\right)\times 100 = (3-1)\times 100 = 200$.

This has the benefit of giving you a fast way to "ballpark" what you're looking for. So if you had, say, 397 as the new value, and 53 as the reference value, then you know that 50 is a little less than 53, so 8*50 is a little less than 8*53. Combine that with the fact that 397 is a little less than 400 = 8*50, and consequently your increase will be a little less than (8-1)*100 = 700.

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Definitely looks easier than my reference formula. Sorry for the late accept. And thanks! –  Jesús Zazueta Aug 27 '13 at 20:36

Dividing 15 by 5 is not difficult. It also helps to know that being 3 times larger means that it has increased by 2 times, which corresponds to 200%. Generally these questions have the numbers chosed to work out easily, so look for opportunities to do things in the easiest order.

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Thanks for the tip! However, what could I do if for example I'm given, say, the numbers 247 as reference and 77 as the comparison value? I think that would slow me down a bit. :P –  Jesús Zazueta Nov 11 '11 at 19:48
If it is multiple choice, you just need to pick the right one, not necessarily find the answer. Rounding is your friend. For 247 vs 77, if you round to 240 vs 80, it is again a factor 3 or 200% increase. Maybe all the other choices are too far away to worry you. As I said, usually these problems are designed either with numbers that are easy to work with or choices that are easy to make. The objective is to see if you know the subject, not to make you do a long division to 5 places. –  Ross Millikan Nov 11 '11 at 20:23