ACT Preparation / Unit 7 ACT 0633 worked example, 60 to 90 seconds
Two Changes in a Row
The idea
To combine two percent changes, work in three steps. First, write each change as a multiplier: an increase of r becomes 1 + r, and a decrease of r becomes 1 − r. Second, multiply the multipliers, in either order, to get the overall multiplier. Third, read the overall change from it: a multiplier above 1 is an increase by the excess, and below 1 a decrease by the shortfall.
In practice
Worked example: a stock rises 25% one year and falls 20% the next. Multipliers: 1.25 and 0.80. Product: 1.25 × 0.80 = 1.00, so the stock ends exactly where it began, though 25 minus 20 suggests a 5% gain. Second: a price rises 10% twice: 1.1 × 1.1 = 1.21, a 21% increase, not 20%.
Where people slip
To undo a percent change, divide by its multiplier rather than reversing the percent: after a 20% drop, getting back needs a 25% rise, because 1 ÷ 0.8 = 1.25.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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