PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022
Percent change
Ratios, proportions, and percents
Data analysis
LEARNING OBJECTIVE
After this lesson, you will be able to:
· Calculate percent change
To answer a question like this:
For three days in a row, Bonnie changes the amount of lemonade made for her lemonade stand. First, she increases the amount made by 25 percent. Then, she decreases it by 10 percent. Finally, she increases it by 35 percent. What is the net percent increase in the amount of lemonade Bonnie made on the third day compared to original amount before the three days of changes, to the nearest whole percent? (The percent sign is understood after your answer. For example, if the answer is 15.1 percent, grid in 15.)
You need to know this:
You can determine the percent change in a given situation by applying this formula:
Sometimes, more than one change will occur. Be careful here, as it can be tempting to take a “shortcut” by just adding two percent changes together (which will almost always lead to an incorrect answer). Instead, you’ll need to find the total amount of the increase or decrease and then apply the formula.
You need to do this:
· Calculate the actual increase or decrease.
· Divide by the original amount (not the new amount!).
· Multiply by 100 percent.
Explanation:
There isn’t any starting number given, so pick 100 and then calculate the actual change. An increase of 25% brings the amount of lemonade made to 125. A 10% decrease from 125 brings the amount of lemonade made to 125 − 12.5 = 112.5. Lastly, an increase of 35% puts the final amount of lemonade made at 112.5 + 0.35(112.5) = 112.5 + 39.375 = 151.875. The actual increase, then, is 151.875 − 100 = 51.875.
Now, plug this increase into the percent change formula, using your starting value of 100 as the denominator:
Round up and grid in 52.
Try on Your Own
Directions: Take as much time as you need on these questions. Work carefully and methodically. There will be an opportunity for timed practice at the end of the chapter.
16. A used car dealership initially prices a car at $12,000. When the car fails to sell, the dealership reduces the price to $10,500. During a holiday sale, the dealership drops the price of the car an additional 5 percent below the reduced price. To the nearest tenth of a percent, what is the total percent discount from the car’s initial price to the holiday sale price?
A. 15.5%
B.16.9%
C.17.5%
D. 20%
HINT: The first thing you’ll want to do for Q17 is figure out how much sand and gravel was sold this year.
17. Last year, a sand and gravel company sold 280 tons of gravel and 220 tons of sand. This year, the company sold 20 percent more gravel by weight and 25 percent more sand by weight than it sold last year. By approximately what percent did the total weight of sand and gravel sold increase this year over last year?
A. 22%
B.45%
C.56%
D. 111%
HINT: Remember that when picking numbers for Q18, you don’t have to pick realistic values. Pick numbers that are easy to work with in the given situation. For percent questions, the number is usually 100.
18. Over the past decade, the population of a certain town increased by 20 percent. If the population of the town increases 15 percent over the next decade, by what percent will the population have increased over the entire two-decade period?
A. 33%
B.35%
C.38%
D. 43%
19. Malik purchased a mutual fund to help save for his daughter’s college costs. During the first year, the price of the fund increased by 15 percent. The following year, the price increased by an additional 12 percent. To the nearest percent, what is the percent increase in the price of the stock for the two years?
A. 24%
B.27%
C.28%
D. 29%
HINT: What information do you need to determine in order to answer Q20 correctly?
20. There are currently 6,210 fish in a lake. If the number of fish in the lake increased by 15 percent during the last year and 20 percent during the year before that, how many more fish are in the lake currently than in the lake two years ago?