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# Percent Increase/Decrease

**23**

Could you provide some "rules" to doing percent increase/decrease? I feel like it is such a simple topic but for some reason, I struggle to figure out the answers to these types of problems because I plug in the wrong numbers to the formulas. And any general advice as to how to tackle these problems would be awesome!

Thanks!

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## Posts

97Great question about a topic that many students struggle with. In the same manner as we try to simplify combinatorics and probability by stripping away some of the accouterments of formal math, percent increase and decrease also benefits from a simplified, systematic approach. However, as I'm sure you know by now, I'm not a fan of just telling students to plug and chug numbers through inscrutable formulas because it's also important to understand the underlying concept to ensure proper application on relevant problems.

With these goals of simplifying the topic but also improving understanding in mind, let's tackle percent change first conceptually and then in an applied manner.

## What is percent change?

Percent change is a measurement of a change in values, going from an initial ("old") value to a final ("new") value. The result of a percent change calculation gives the amount by which we have changed this old value expressed as a fraction, the percent of the old value we changed to arrive at the new value.This might sound complicated, so let's use an example to illustrate.

Say we started with 50 ding-dongs and went to the convenience store to buy 25 more. By what percent did the number of ding-dongs we have increase, assuming we ate no ding-dongs?

Solution:

Start with the initial value of 50 ding-dongs. Now consider the final value, 75 ding-dongs. How many more ding-dongs do we have now? 25 more. This value of 25 is the change in ding-dongs. It is the actual number. We need to convert this actual number into a percent

relativeto the initial value of 50. Why? Because that's what we started with!Express the change in number of ding-dongs (25) as the dividend/numerator of our fraction (this is the

partthat changed).Express the initial number of ding-dongs (50) as the divisor/denominator of our fraction (this is the

wholethat we began with).25 ÷ 50 = ½

Well, ½ isn't a percent yet. How do we express the fraction ½ as a percent? Multiply by 100!

½ = 0.50

0.50 x 100 = 50

Thus we have a percent

increaseof 50%.How do we know it's a percent increase (as opposed to percent decrease)? We know this because our initial/old number was smaller. That value went up to reach our final/new number.

## Important observations

From this example, let's move on to a couple general rules:percent increase, the initial number is always smaller. In the event that it'spercent decrease, the initial number is always bigger.Let's pause and consider point 3 for a moment:

If there is more than one change in values, you must "reset" your calculations each time, changing initial and final values.

What does this mean in practice? Let's return to our ding-dong example.

We started out with 50 ding-dongs. We went to the store and bought 25 more. Then we ate 15 ding dongs. By what percent did our ding-dongs decrease after our purchase?

Solution:

Now we ask, is our initial value 50 ding-dongs or 75 ding-dongs? Read exactly what the question asks. Our initial value for the purpose of this percent change is the number of ding-dongs after our purchase (75). Thus, the formula is:

(Difference in Numbers)/(Initial Number) x 100

15 ÷ 75 = 1/5 = 0.20 = 20%

Notice we now had a percent decrease. The initial number (75) was bigger than the final number (60). We had a 20% decrease in ding-dongs.

## Put it all together

The GRE will sometimes combine all the above concepts into a longer, multi-step question. Let's take a look at how this might appear on the GRE:Josie had 50 ding-dongs and went to the convenience store to buy 25 more. She subsequently went on a ding-dong eating bonanza and consumed 30 ding-dongs before being rushed to the emergency room. When all was said and done, what was the percent change in Josie's ding-dongs relative to what she started out with?

Solution:

Start with her 50 ding-dongs.

Now we go up to 75.

Now we go back down to 45.

We have to decide what our initial and final values are. The initial value according the the question is what she started out with, 50. The final value is what she ended up with, 45. The difference in these numbers is 5. Let's use our formula:

5 ÷ 50 = 1/10 = 0.10 = 10%

I hope this helps!

23Helps a lot

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