Question

What single percentage change is equivalent to a 23% decrease followed by a 16% increase?

Answer 1

Answer:  10.68% decrease (choice F)

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Explanation:

A decrease of 23% means that you still retain 77% of the original value. This is because 23% + 77% = 100%. Or you could write it like this: 100% - 23% = 77%. The 77% then converts to the multiplier 0.77

An increase of 16% will involve the multiplier 1.16 in which we can think of it like 1.16 = 1 + 0.16 = 100% + 16%

Now we'll multiply those two decimal values mentioned:

0.77*1.16 = 0.8932

This result is smaller than 1, so we have a percent decrease of some sort. Subtract it from 1 to find the decimal form of the percent decrease

1 - 0.8932 = 0.1068

Lastly, move the decimal point 2 spots to the right:

0.1068 converts to 10.68%

We have a decrease of 10.68% overall when combining the initial 23% decrease followed by the 16% increase.

It turns out the order doesn't matter, and we could do the 16% increase first then the 23% decrease next. The key as to why the order doesn't matter all relies on the fact that multiplication can be done in any order. As you can probably guess, this process can be extended for as many percentage increases and/or decreases that you want.