Percents and percent change

Example 1

1. First, decide which question is being asked. “By what percent” asks how big the change was for its size, not how many dollars. So this is a percent change.
2. Find the change, a plain subtraction: $1,204 − $1,159 = $45. That is a count of dollars. Choice A offers it as a percent, the most common trap: 45 is how many dollars, not how many per hundred.
3. Now ask: percent of what? Percent change always compares the change with the old value, the place where you started. Here that is the 2024 figure, $1,159.
4. Divide: 45 ÷ 1,159. To work it by hand, round: 1 percent of 1,159 is about 11.6, and 45 is a little less than 4 of those (4 × 11.6 = 46.4). So the rise is a little less than 4 percent. Exactly, 45 ÷ 1,159 = 0.0388, about 3.9 percent. That is C.
5. Both ways are worth knowing. The test gives you an on-screen calculator, and working by hand lets you check that the calculator’s answer makes sense. On the calculator: type ( 1204 − 1159 ) ÷ 1159 and press enter. The parentheses make the calculator subtract first. The screen shows 0.038826...; move the decimal point two places to the right: about 3.9 percent. It agrees with the by-hand answer, a little less than 4 percent. Type the numbers without commas; the calculator has no comma key. If the screen shows a fraction instead of a decimal, press the toggle key to change it to a decimal.
6. B comes from dividing by the new value: 45 ÷ 1,204 = 0.037, about 3.7 percent. It is close, which is what makes it a trap. The rule settles it: divide by the old value.
7. D comes from 1,204 ÷ 1,159 = 1.039, read as 104 percent. That is the new value as a percent of the old one. The rise is the part above 100 percent: about 3.9.
8. Check the answer the other way: 3.9 percent of $1,159 is about $45. It matches.

Answer: C

Example 2

1. Two different numbers can describe this change, and the test asks you to keep them apart.
2. The first is percentage points: a plain subtraction of the two percents. 30 − 20 = 10 percentage points.
3. The second is percent change: the change compared with the old value. 10 ÷ 20 = 0.5, which is 50 percent. The share grew by half of itself.
4. On the calculator: type ( 30 − 20 ) ÷ 20 and press enter. The screen shows 0.5; move the decimal point two places to the right: 50 percent. The percentage points need no calculator: 30 − 20 is a plain subtraction.
5. Picture one row of a hundred adults. Before, 20 of them had a card; after, 30 did. Ten more people in the row: 10 points. And 10 more on top of 20 is half again as many: 50 percent.
6. Now the choices. A takes the 10 points and calls them 10 percent. That mixes up the two numbers. C gives the new share, 30 percent, as if it were the change. D takes the 50 percent and calls it points.
7. B says both numbers, each with its right name. That is the answer.

Answer: B