Rates and per capita

Example 1

1. First habit: decide which question is asked. “How many crashes” would be a count question. “The higher rate for its number of residents” asks how common crashes were. That is a rate question.
2. A count by itself is hard to compare here, because the neighborhoods are different sizes. Riverside has four times as many people as Hilltop.
3. So put each count on the same base. Crashes are few compared with people, so a base of 1,000 people gives numbers that are easy to picture.
4. Riverside: 40,000 residents is 40 groups of 1,000. 120 ÷ 40 = 3 crashes per 1,000 residents.
5. Hilltop: 10,000 residents is 10 groups of 1,000. 50 ÷ 10 = 5 crashes per 1,000 residents.
6. 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: divide the count by the whole, then multiply by the base, 1,000. Type 120 ÷ 40000 × 1000 and press enter. The screen shows 3. Type 50 ÷ 10000 × 1000 and press enter. The screen shows 5. The same rates as by hand. 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.
7. 5 is higher than 3, so Hilltop had the higher rate. That is B.
8. A answers “how many” when the question asked “how common”: the count in place of the rate. D says it cannot be told, but the counts and the sizes are both given, and they are all a rate needs.

Answer: B

Example 2

1. This is a per question: people per seat. Each state’s people are shared among its seats, so divide the people by the seats.
2. California: 39,576,757 ÷ 52 = about 761,091 people per seat.
3. Texas: 29,183,290 ÷ 38 = about 767,981 people per seat.
4. These divisions are long to do by hand. To check them without a calculator, multiply back with rounded numbers: 52 × 761,000 is about 39.6 million, and 38 × 768,000 is about 29.2 million. Both match the counts in the table.
5. On the calculator: type 39576757 ÷ 52 and press enter. The screen shows 761091.48...; that is about 761,091 people per seat. Type 29183290 ÷ 38 and press enter. The screen shows 767981.31...; that is about 767,981. The rounded check above shows these answers make sense.
6. Texas has about 7,000 more people per seat. That is C.
7. A uses the count of people alone. California has more people, but it also has more seats to share them among. B uses the count of seats alone. Neither count answers a per question by itself.
8. D is close to true, since the two numbers differ by less than 1 percent, but they are not the same. The question asks which is more, and Texas is.

Answer: C